Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces

Abstract We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embe...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Clavero, Nadia [verfasserIn] Soria, Javier

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	Sobolev embeddings Rearrangement-invariant spaces Hardy operator Optimal range Optimal domain

Anmerkung:	© Mathematica Josephina, Inc. 2015

Übergeordnetes Werk:	Enthalten in: The journal of geometric analysis - New York, NY : Springer, 1991, 26(2015), 4 vom: 13. Nov., Seite 2930-2954
Übergeordnetes Werk:	volume:26 ; year:2015 ; number:4 ; day:13 ; month:11 ; pages:2930-2954

Links:	Volltext

DOI / URN:	10.1007/s12220-015-9655-x

Katalog-ID:	SPR025408283

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520			\|a Abstract We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space %$W^{1}L^{p}%$ by Poornima (Bull Sci Math 107(3):253–259, 1983), O’Neil (Duke Math J 30:129–142, 1963) and Peetre (Ann Inst Fourier 16(1):279–317, 1966) (%$1 \le p < n%$), and by Hansson (Math Scand 45(1):77–102, 1979, Brezis and Wainger (Commun Partial Differ Equ 5(7):773–789, 1980) and Maz’ya (Sobolev spaces, 1985) (%$p=n%$) can be further strengthened by considering mixed norms on the target spaces.
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650		4	\|a Rearrangement-invariant spaces \|7 (dpeaa)DE-He213
650		4	\|a Hardy operator \|7 (dpeaa)DE-He213
650		4	\|a Optimal range \|7 (dpeaa)DE-He213
650		4	\|a Optimal domain \|7 (dpeaa)DE-He213
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912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
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912			\|a GBV_ILN_95
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912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
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912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
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912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
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912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
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912			\|a GBV_ILN_4336
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matchkey_str	article:1559002X:2015----::piararneetnainsblvmedn
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publishDate	2015
allfields	10.1007/s12220-015-9655-x doi (DE-627)SPR025408283 (SPR)s12220-015-9655-x-e DE-627 ger DE-627 rakwb eng Clavero, Nadia verfasserin aut Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2015 Abstract We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space %$W^{1}L^{p}%$ by Poornima (Bull Sci Math 107(3):253–259, 1983), O’Neil (Duke Math J 30:129–142, 1963) and Peetre (Ann Inst Fourier 16(1):279–317, 1966) (%$1 \le p < n%$), and by Hansson (Math Scand 45(1):77–102, 1979, Brezis and Wainger (Commun Partial Differ Equ 5(7):773–789, 1980) and Maz’ya (Sobolev spaces, 1985) (%$p=n%$) can be further strengthened by considering mixed norms on the target spaces. Sobolev embeddings (dpeaa)DE-He213 Rearrangement-invariant spaces (dpeaa)DE-He213 Hardy operator (dpeaa)DE-He213 Optimal range (dpeaa)DE-He213 Optimal domain (dpeaa)DE-He213 Soria, Javier aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 26(2015), 4 vom: 13. Nov., Seite 2930-2954 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:26 year:2015 number:4 day:13 month:11 pages:2930-2954 https://dx.doi.org/10.1007/s12220-015-9655-x 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_65 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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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 26 2015 4 13 11 2930-2954
spelling	10.1007/s12220-015-9655-x doi (DE-627)SPR025408283 (SPR)s12220-015-9655-x-e DE-627 ger DE-627 rakwb eng Clavero, Nadia verfasserin aut Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2015 Abstract We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space %$W^{1}L^{p}%$ by Poornima (Bull Sci Math 107(3):253–259, 1983), O’Neil (Duke Math J 30:129–142, 1963) and Peetre (Ann Inst Fourier 16(1):279–317, 1966) (%$1 \le p < n%$), and by Hansson (Math Scand 45(1):77–102, 1979, Brezis and Wainger (Commun Partial Differ Equ 5(7):773–789, 1980) and Maz’ya (Sobolev spaces, 1985) (%$p=n%$) can be further strengthened by considering mixed norms on the target spaces. Sobolev embeddings (dpeaa)DE-He213 Rearrangement-invariant spaces (dpeaa)DE-He213 Hardy operator (dpeaa)DE-He213 Optimal range (dpeaa)DE-He213 Optimal domain (dpeaa)DE-He213 Soria, Javier aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 26(2015), 4 vom: 13. Nov., Seite 2930-2954 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:26 year:2015 number:4 day:13 month:11 pages:2930-2954 https://dx.doi.org/10.1007/s12220-015-9655-x 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_65 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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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 26 2015 4 13 11 2930-2954
allfields_unstemmed	10.1007/s12220-015-9655-x doi (DE-627)SPR025408283 (SPR)s12220-015-9655-x-e DE-627 ger DE-627 rakwb eng Clavero, Nadia verfasserin aut Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2015 Abstract We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space %$W^{1}L^{p}%$ by Poornima (Bull Sci Math 107(3):253–259, 1983), O’Neil (Duke Math J 30:129–142, 1963) and Peetre (Ann Inst Fourier 16(1):279–317, 1966) (%$1 \le p < n%$), and by Hansson (Math Scand 45(1):77–102, 1979, Brezis and Wainger (Commun Partial Differ Equ 5(7):773–789, 1980) and Maz’ya (Sobolev spaces, 1985) (%$p=n%$) can be further strengthened by considering mixed norms on the target spaces. Sobolev embeddings (dpeaa)DE-He213 Rearrangement-invariant spaces (dpeaa)DE-He213 Hardy operator (dpeaa)DE-He213 Optimal range (dpeaa)DE-He213 Optimal domain (dpeaa)DE-He213 Soria, Javier aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 26(2015), 4 vom: 13. Nov., Seite 2930-2954 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:26 year:2015 number:4 day:13 month:11 pages:2930-2954 https://dx.doi.org/10.1007/s12220-015-9655-x 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_65 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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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 26 2015 4 13 11 2930-2954
allfieldsGer	10.1007/s12220-015-9655-x doi (DE-627)SPR025408283 (SPR)s12220-015-9655-x-e DE-627 ger DE-627 rakwb eng Clavero, Nadia verfasserin aut Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2015 Abstract We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space %$W^{1}L^{p}%$ by Poornima (Bull Sci Math 107(3):253–259, 1983), O’Neil (Duke Math J 30:129–142, 1963) and Peetre (Ann Inst Fourier 16(1):279–317, 1966) (%$1 \le p < n%$), and by Hansson (Math Scand 45(1):77–102, 1979, Brezis and Wainger (Commun Partial Differ Equ 5(7):773–789, 1980) and Maz’ya (Sobolev spaces, 1985) (%$p=n%$) can be further strengthened by considering mixed norms on the target spaces. Sobolev embeddings (dpeaa)DE-He213 Rearrangement-invariant spaces (dpeaa)DE-He213 Hardy operator (dpeaa)DE-He213 Optimal range (dpeaa)DE-He213 Optimal domain (dpeaa)DE-He213 Soria, Javier aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 26(2015), 4 vom: 13. Nov., Seite 2930-2954 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:26 year:2015 number:4 day:13 month:11 pages:2930-2954 https://dx.doi.org/10.1007/s12220-015-9655-x 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_65 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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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 26 2015 4 13 11 2930-2954
allfieldsSound	10.1007/s12220-015-9655-x doi (DE-627)SPR025408283 (SPR)s12220-015-9655-x-e DE-627 ger DE-627 rakwb eng Clavero, Nadia verfasserin aut Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2015 Abstract We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space %$W^{1}L^{p}%$ by Poornima (Bull Sci Math 107(3):253–259, 1983), O’Neil (Duke Math J 30:129–142, 1963) and Peetre (Ann Inst Fourier 16(1):279–317, 1966) (%$1 \le p < n%$), and by Hansson (Math Scand 45(1):77–102, 1979, Brezis and Wainger (Commun Partial Differ Equ 5(7):773–789, 1980) and Maz’ya (Sobolev spaces, 1985) (%$p=n%$) can be further strengthened by considering mixed norms on the target spaces. Sobolev embeddings (dpeaa)DE-He213 Rearrangement-invariant spaces (dpeaa)DE-He213 Hardy operator (dpeaa)DE-He213 Optimal range (dpeaa)DE-He213 Optimal domain (dpeaa)DE-He213 Soria, Javier aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 26(2015), 4 vom: 13. Nov., Seite 2930-2954 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:26 year:2015 number:4 day:13 month:11 pages:2930-2954 https://dx.doi.org/10.1007/s12220-015-9655-x 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_65 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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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 26 2015 4 13 11 2930-2954
language	English
source	Enthalten in The journal of geometric analysis 26(2015), 4 vom: 13. Nov., Seite 2930-2954 volume:26 year:2015 number:4 day:13 month:11 pages:2930-2954
sourceStr	Enthalten in The journal of geometric analysis 26(2015), 4 vom: 13. Nov., Seite 2930-2954 volume:26 year:2015 number:4 day:13 month:11 pages:2930-2954
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Sobolev embeddings Rearrangement-invariant spaces Hardy operator Optimal range Optimal domain
isfreeaccess_bool	false
container_title	The journal of geometric analysis
authorswithroles_txt_mv	Clavero, Nadia @@aut@@ Soria, Javier @@aut@@
publishDateDaySort_date	2015-11-13T00:00:00Z
hierarchy_top_id	496971867
id	SPR025408283
language_de	englisch
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author	Clavero, Nadia
spellingShingle	Clavero, Nadia misc Sobolev embeddings misc Rearrangement-invariant spaces misc Hardy operator misc Optimal range misc Optimal domain Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces
authorStr	Clavero, Nadia
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topic_title	Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces Sobolev embeddings (dpeaa)DE-He213 Rearrangement-invariant spaces (dpeaa)DE-He213 Hardy operator (dpeaa)DE-He213 Optimal range (dpeaa)DE-He213 Optimal domain (dpeaa)DE-He213
topic	misc Sobolev embeddings misc Rearrangement-invariant spaces misc Hardy operator misc Optimal range misc Optimal domain
topic_unstemmed	misc Sobolev embeddings misc Rearrangement-invariant spaces misc Hardy operator misc Optimal range misc Optimal domain
topic_browse	misc Sobolev embeddings misc Rearrangement-invariant spaces misc Hardy operator misc Optimal range misc Optimal domain
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title	Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces
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title_full	Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces
author_sort	Clavero, Nadia
journal	The journal of geometric analysis
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author_browse	Clavero, Nadia Soria, Javier
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author-letter	Clavero, Nadia
doi_str_mv	10.1007/s12220-015-9655-x
title_sort	optimal rearrangement invariant sobolev embeddings in mixed norm spaces
title_auth	Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces
abstract	Abstract We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space %$W^{1}L^{p}%$ by Poornima (Bull Sci Math 107(3):253–259, 1983), O’Neil (Duke Math J 30:129–142, 1963) and Peetre (Ann Inst Fourier 16(1):279–317, 1966) (%$1 \le p < n%$), and by Hansson (Math Scand 45(1):77–102, 1979, Brezis and Wainger (Commun Partial Differ Equ 5(7):773–789, 1980) and Maz’ya (Sobolev spaces, 1985) (%$p=n%$) can be further strengthened by considering mixed norms on the target spaces. © Mathematica Josephina, Inc. 2015
abstractGer	Abstract We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space %$W^{1}L^{p}%$ by Poornima (Bull Sci Math 107(3):253–259, 1983), O’Neil (Duke Math J 30:129–142, 1963) and Peetre (Ann Inst Fourier 16(1):279–317, 1966) (%$1 \le p < n%$), and by Hansson (Math Scand 45(1):77–102, 1979, Brezis and Wainger (Commun Partial Differ Equ 5(7):773–789, 1980) and Maz’ya (Sobolev spaces, 1985) (%$p=n%$) can be further strengthened by considering mixed norms on the target spaces. © Mathematica Josephina, Inc. 2015
abstract_unstemmed	Abstract We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space %$W^{1}L^{p}%$ by Poornima (Bull Sci Math 107(3):253–259, 1983), O’Neil (Duke Math J 30:129–142, 1963) and Peetre (Ann Inst Fourier 16(1):279–317, 1966) (%$1 \le p < n%$), and by Hansson (Math Scand 45(1):77–102, 1979, Brezis and Wainger (Commun Partial Differ Equ 5(7):773–789, 1980) and Maz’ya (Sobolev spaces, 1985) (%$p=n%$) can be further strengthened by considering mixed norms on the target spaces. © Mathematica Josephina, Inc. 2015
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container_issue	4
title_short	Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces
url	https://dx.doi.org/10.1007/s12220-015-9655-x
remote_bool	true
author2	Soria, Javier
author2Str	Soria, Javier
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doi_str	10.1007/s12220-015-9655-x
up_date	2024-07-03T15:49:13.337Z
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score	7.402011

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Optimal Rearrangement Invariant Sobolev Embeddings in Mixed Norm Spaces

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