Multilinear Marcinkiewicz-Zygmund Inequalities
Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operat...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Carando, Daniel [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC 2017 |
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| Übergeordnetes Werk: |
Enthalten in: The journal of Fourier analysis and applications - Cambridge, Mass. : Birkhäuser Boston, 1994, 25(2017), 1 vom: 12. Sept., Seite 51-85 |
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| Übergeordnetes Werk: |
volume:25 ; year:2017 ; number:1 ; day:12 ; month:09 ; pages:51-85 |
| Links: |
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| DOI / URN: |
10.1007/s00041-017-9563-5 |
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| Katalog-ID: |
SPR000379948 |
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| 100 | 1 | |a Carando, Daniel |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Multilinear Marcinkiewicz-Zygmund Inequalities |
| 264 | 1 | |c 2017 | |
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| 520 | |a Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operator %$T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )%$ and functions %$\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)%$, the following inequality holds 1∑k1,⋯,km|T(fk11,⋯,fkmm)|r1/rLp(ν)≤C‖T‖∏i=1m∑ki=1ni|fkii|r1/rLqi(μi).%$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}%$In some cases we also calculate the best constant %$C\ge 0%$ satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. | ||
| 650 | 4 | |a Vector-valued inequalities |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Multilinear operators |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Calderón-Zygmund operators |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Mazzitelli, Martin |4 aut | |
| 700 | 1 | |a Ombrosi, Sheldy |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t The journal of Fourier analysis and applications |d Cambridge, Mass. : Birkhäuser Boston, 1994 |g 25(2017), 1 vom: 12. Sept., Seite 51-85 |w (DE-627)326360484 |w (DE-600)2042054-7 |x 1531-5851 |7 nnns |
| 773 | 1 | 8 | |g volume:25 |g year:2017 |g number:1 |g day:12 |g month:09 |g pages:51-85 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00041-017-9563-5 |z lizenzpflichtig |3 Volltext |
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| 952 | |d 25 |j 2017 |e 1 |b 12 |c 09 |h 51-85 | ||
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2017 |
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2017 |
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10.1007/s00041-017-9563-5 doi (DE-627)SPR000379948 (SPR)s00041-017-9563-5-e DE-627 ger DE-627 rakwb eng Carando, Daniel verfasserin aut Multilinear Marcinkiewicz-Zygmund Inequalities 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC 2017 Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operator %$T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )%$ and functions %$\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)%$, the following inequality holds 1∑k1,⋯,km|T(fk11,⋯,fkmm)|r1/rLp(ν)≤C‖T‖∏i=1m∑ki=1ni|fkii|r1/rLqi(μi).%$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}%$In some cases we also calculate the best constant %$C\ge 0%$ satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. Vector-valued inequalities (dpeaa)DE-He213 Multilinear operators (dpeaa)DE-He213 Calderón-Zygmund operators (dpeaa)DE-He213 Mazzitelli, Martin aut Ombrosi, Sheldy aut Enthalten in The journal of Fourier analysis and applications Cambridge, Mass. : Birkhäuser Boston, 1994 25(2017), 1 vom: 12. Sept., Seite 51-85 (DE-627)326360484 (DE-600)2042054-7 1531-5851 nnns volume:25 year:2017 number:1 day:12 month:09 pages:51-85 https://dx.doi.org/10.1007/s00041-017-9563-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2017 1 12 09 51-85 |
| spelling |
10.1007/s00041-017-9563-5 doi (DE-627)SPR000379948 (SPR)s00041-017-9563-5-e DE-627 ger DE-627 rakwb eng Carando, Daniel verfasserin aut Multilinear Marcinkiewicz-Zygmund Inequalities 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC 2017 Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operator %$T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )%$ and functions %$\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)%$, the following inequality holds 1∑k1,⋯,km|T(fk11,⋯,fkmm)|r1/rLp(ν)≤C‖T‖∏i=1m∑ki=1ni|fkii|r1/rLqi(μi).%$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}%$In some cases we also calculate the best constant %$C\ge 0%$ satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. Vector-valued inequalities (dpeaa)DE-He213 Multilinear operators (dpeaa)DE-He213 Calderón-Zygmund operators (dpeaa)DE-He213 Mazzitelli, Martin aut Ombrosi, Sheldy aut Enthalten in The journal of Fourier analysis and applications Cambridge, Mass. : Birkhäuser Boston, 1994 25(2017), 1 vom: 12. Sept., Seite 51-85 (DE-627)326360484 (DE-600)2042054-7 1531-5851 nnns volume:25 year:2017 number:1 day:12 month:09 pages:51-85 https://dx.doi.org/10.1007/s00041-017-9563-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2017 1 12 09 51-85 |
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10.1007/s00041-017-9563-5 doi (DE-627)SPR000379948 (SPR)s00041-017-9563-5-e DE-627 ger DE-627 rakwb eng Carando, Daniel verfasserin aut Multilinear Marcinkiewicz-Zygmund Inequalities 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC 2017 Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operator %$T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )%$ and functions %$\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)%$, the following inequality holds 1∑k1,⋯,km|T(fk11,⋯,fkmm)|r1/rLp(ν)≤C‖T‖∏i=1m∑ki=1ni|fkii|r1/rLqi(μi).%$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}%$In some cases we also calculate the best constant %$C\ge 0%$ satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. Vector-valued inequalities (dpeaa)DE-He213 Multilinear operators (dpeaa)DE-He213 Calderón-Zygmund operators (dpeaa)DE-He213 Mazzitelli, Martin aut Ombrosi, Sheldy aut Enthalten in The journal of Fourier analysis and applications Cambridge, Mass. : Birkhäuser Boston, 1994 25(2017), 1 vom: 12. Sept., Seite 51-85 (DE-627)326360484 (DE-600)2042054-7 1531-5851 nnns volume:25 year:2017 number:1 day:12 month:09 pages:51-85 https://dx.doi.org/10.1007/s00041-017-9563-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2017 1 12 09 51-85 |
| allfieldsGer |
10.1007/s00041-017-9563-5 doi (DE-627)SPR000379948 (SPR)s00041-017-9563-5-e DE-627 ger DE-627 rakwb eng Carando, Daniel verfasserin aut Multilinear Marcinkiewicz-Zygmund Inequalities 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC 2017 Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operator %$T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )%$ and functions %$\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)%$, the following inequality holds 1∑k1,⋯,km|T(fk11,⋯,fkmm)|r1/rLp(ν)≤C‖T‖∏i=1m∑ki=1ni|fkii|r1/rLqi(μi).%$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}%$In some cases we also calculate the best constant %$C\ge 0%$ satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. Vector-valued inequalities (dpeaa)DE-He213 Multilinear operators (dpeaa)DE-He213 Calderón-Zygmund operators (dpeaa)DE-He213 Mazzitelli, Martin aut Ombrosi, Sheldy aut Enthalten in The journal of Fourier analysis and applications Cambridge, Mass. : Birkhäuser Boston, 1994 25(2017), 1 vom: 12. Sept., Seite 51-85 (DE-627)326360484 (DE-600)2042054-7 1531-5851 nnns volume:25 year:2017 number:1 day:12 month:09 pages:51-85 https://dx.doi.org/10.1007/s00041-017-9563-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2017 1 12 09 51-85 |
| allfieldsSound |
10.1007/s00041-017-9563-5 doi (DE-627)SPR000379948 (SPR)s00041-017-9563-5-e DE-627 ger DE-627 rakwb eng Carando, Daniel verfasserin aut Multilinear Marcinkiewicz-Zygmund Inequalities 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC 2017 Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operator %$T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )%$ and functions %$\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)%$, the following inequality holds 1∑k1,⋯,km|T(fk11,⋯,fkmm)|r1/rLp(ν)≤C‖T‖∏i=1m∑ki=1ni|fkii|r1/rLqi(μi).%$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}%$In some cases we also calculate the best constant %$C\ge 0%$ satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. Vector-valued inequalities (dpeaa)DE-He213 Multilinear operators (dpeaa)DE-He213 Calderón-Zygmund operators (dpeaa)DE-He213 Mazzitelli, Martin aut Ombrosi, Sheldy aut Enthalten in The journal of Fourier analysis and applications Cambridge, Mass. : Birkhäuser Boston, 1994 25(2017), 1 vom: 12. Sept., Seite 51-85 (DE-627)326360484 (DE-600)2042054-7 1531-5851 nnns volume:25 year:2017 number:1 day:12 month:09 pages:51-85 https://dx.doi.org/10.1007/s00041-017-9563-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2017 1 12 09 51-85 |
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English |
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Enthalten in The journal of Fourier analysis and applications 25(2017), 1 vom: 12. Sept., Seite 51-85 volume:25 year:2017 number:1 day:12 month:09 pages:51-85 |
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Enthalten in The journal of Fourier analysis and applications 25(2017), 1 vom: 12. Sept., Seite 51-85 volume:25 year:2017 number:1 day:12 month:09 pages:51-85 |
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Vector-valued inequalities Multilinear operators Calderón-Zygmund operators |
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Carando, Daniel @@aut@@ Mazzitelli, Martin @@aut@@ Ombrosi, Sheldy @@aut@@ |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR000379948</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230330084217.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2017 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00041-017-9563-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR000379948</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00041-017-9563-5-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Carando, Daniel</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Multilinear Marcinkiewicz-Zygmund Inequalities</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, LLC 2017</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operator %$T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )%$ and functions %$\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)%$, the following inequality holds 1∑k1,⋯,km|T(fk11,⋯,fkmm)|r1/rLp(ν)≤C‖T‖∏i=1m∑ki=1ni|fkii|r1/rLqi(μi).%$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}%$In some cases we also calculate the best constant %$C\ge 0%$ satisfying the previous inequality. 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Carando, Daniel |
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Carando, Daniel misc Vector-valued inequalities misc Multilinear operators misc Calderón-Zygmund operators Multilinear Marcinkiewicz-Zygmund Inequalities |
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Multilinear Marcinkiewicz-Zygmund Inequalities Vector-valued inequalities (dpeaa)DE-He213 Multilinear operators (dpeaa)DE-He213 Calderón-Zygmund operators (dpeaa)DE-He213 |
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misc Vector-valued inequalities misc Multilinear operators misc Calderón-Zygmund operators |
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Multilinear Marcinkiewicz-Zygmund Inequalities |
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multilinear marcinkiewicz-zygmund inequalities |
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Multilinear Marcinkiewicz-Zygmund Inequalities |
| abstract |
Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operator %$T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )%$ and functions %$\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)%$, the following inequality holds 1∑k1,⋯,km|T(fk11,⋯,fkmm)|r1/rLp(ν)≤C‖T‖∏i=1m∑ki=1ni|fkii|r1/rLqi(μi).%$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}%$In some cases we also calculate the best constant %$C\ge 0%$ satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. © Springer Science+Business Media, LLC 2017 |
| abstractGer |
Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operator %$T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )%$ and functions %$\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)%$, the following inequality holds 1∑k1,⋯,km|T(fk11,⋯,fkmm)|r1/rLp(ν)≤C‖T‖∏i=1m∑ki=1ni|fkii|r1/rLqi(μi).%$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}%$In some cases we also calculate the best constant %$C\ge 0%$ satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. © Springer Science+Business Media, LLC 2017 |
| abstract_unstemmed |
Abstract We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on %$\ell ^r%$-valued extensions of linear operators. We show that for certain %$1 \le p, q_1, \dots , q_m, r \le \infty %$, there is a constant %$C\ge 0%$ such that for every bounded multilinear operator %$T:L^{q_1}(\mu _1) \times \cdots \times L^{q_m}(\mu _m) \rightarrow L^p(\nu )%$ and functions %$\{f_{k_1}^1\}_{k_1=1}^{n_1} \subset L^{q_1}(\mu _1), \dots , \{f_{k_m}^m\}_{k_m=1}^{n_m} \subset L^{q_m}(\mu _m)%$, the following inequality holds 1∑k1,⋯,km|T(fk11,⋯,fkmm)|r1/rLp(ν)≤C‖T‖∏i=1m∑ki=1ni|fkii|r1/rLqi(μi).%$\begin{aligned} \left\| \left( \sum _{k_1, \dots , k_m} |T(f_{k_1}^1, \dots , f_{k_m}^m)|^r\right) ^{1/r} \right\| _{L^p(\nu )} \le C \Vert T\Vert \prod _{i=1}^m \left\| \left( \sum _{k_i=1}^{n_i} |f_{k_i}^i|^r\right) ^{1/r} \right\| _{L^{q_i}(\mu _i)}. \end{aligned}%$In some cases we also calculate the best constant %$C\ge 0%$ satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. © Springer Science+Business Media, LLC 2017 |
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1 |
| title_short |
Multilinear Marcinkiewicz-Zygmund Inequalities |
| url |
https://dx.doi.org/10.1007/s00041-017-9563-5 |
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true |
| author2 |
Mazzitelli, Martin Ombrosi, Sheldy |
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Mazzitelli, Martin Ombrosi, Sheldy |
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| doi_str |
10.1007/s00041-017-9563-5 |
| up_date |
2024-07-03T15:40:52.723Z |
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1803573005101563904 |
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| score |
7.399081 |