Rough maximal bilinear singular integrals

Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/|(y,z)|)|(y,z)|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb...
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Autor*in:	Buriánková, Eva [verfasserIn] Honzík, Petr

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Singular integrals Bilinear operators Maximal operators Fourier multipliers

Anmerkung:	© Universitat de Barcelona 2019

Übergeordnetes Werk:	Enthalten in: Collectanea mathematica - Barcelona, 1948, 70(2019), 3 vom: 31. Jan., Seite 431-446
Übergeordnetes Werk:	volume:70 ; year:2019 ; number:3 ; day:31 ; month:01 ; pages:431-446

Links:	Volltext

DOI / URN:	10.1007/s13348-019-00239-4

Katalog-ID:	SPR031420079

Internformat


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520			\|a Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/\|(y,z)\|)\|(y,z)\|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left\| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/\|(y,z)\|)}{ \|(y,z)\|^{2n}}f(x-y)g(x-z) dydz\right\| , \end{aligned}%$where %$\varOmega %$ is a function in %$L^\infty (\mathbb S^{2n-1})%$ with vanishing integral. We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$.
650		4	\|a Singular integrals \|7 (dpeaa)DE-He213
650		4	\|a Bilinear operators \|7 (dpeaa)DE-He213
650		4	\|a Maximal operators \|7 (dpeaa)DE-He213
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700	1		\|a Honzík, Petr \|0 (orcid)0000-0001-6545-6461 \|4 aut
773	0	8	\|i Enthalten in \|t Collectanea mathematica \|d Barcelona, 1948 \|g 70(2019), 3 vom: 31. Jan., Seite 431-446 \|w (DE-627)327535180 \|w (DE-600)2044536-2 \|x 2038-4815 \|7 nnns
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856	4	0	\|u https://dx.doi.org/10.1007/s13348-019-00239-4 \|z lizenzpflichtig \|3 Volltext
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912			\|a GBV_ILN_110
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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
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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
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912			\|a GBV_ILN_2001
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912			\|a GBV_ILN_2006
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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
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912			\|a GBV_ILN_2044
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912			\|a GBV_ILN_2049
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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
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912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
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912			\|a GBV_ILN_2153
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Indexfelder

author_variant	e b eb p h ph
matchkey_str	article:20384815:2019----::ogmxmliierigl
hierarchy_sort_str	2019
publishDate	2019
allfields	10.1007/s13348-019-00239-4 doi (DE-627)SPR031420079 (SPR)s13348-019-00239-4-e DE-627 ger DE-627 rakwb eng Buriánková, Eva verfasserin (orcid)0000-0002-3491-0761 aut Rough maximal bilinear singular integrals 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Universitat de Barcelona 2019 Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/\|(y,z)\|)\|(y,z)\|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left\| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/\|(y,z)\|)}{ \|(y,z)\|^{2n}}f(x-y)g(x-z) dydz\right\| , \end{aligned}%$where %$\varOmega %$ is a function in %$L^\infty (\mathbb S^{2n-1})%$ with vanishing integral. We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$. Singular integrals (dpeaa)DE-He213 Bilinear operators (dpeaa)DE-He213 Maximal operators (dpeaa)DE-He213 Fourier multipliers (dpeaa)DE-He213 Honzík, Petr (orcid)0000-0001-6545-6461 aut Enthalten in Collectanea mathematica Barcelona, 1948 70(2019), 3 vom: 31. Jan., Seite 431-446 (DE-627)327535180 (DE-600)2044536-2 2038-4815 nnns volume:70 year:2019 number:3 day:31 month:01 pages:431-446 https://dx.doi.org/10.1007/s13348-019-00239-4 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 70 2019 3 31 01 431-446
spelling	10.1007/s13348-019-00239-4 doi (DE-627)SPR031420079 (SPR)s13348-019-00239-4-e DE-627 ger DE-627 rakwb eng Buriánková, Eva verfasserin (orcid)0000-0002-3491-0761 aut Rough maximal bilinear singular integrals 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Universitat de Barcelona 2019 Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/\|(y,z)\|)\|(y,z)\|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left\| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/\|(y,z)\|)}{ \|(y,z)\|^{2n}}f(x-y)g(x-z) dydz\right\| , \end{aligned}%$where %$\varOmega %$ is a function in %$L^\infty (\mathbb S^{2n-1})%$ with vanishing integral. We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$. Singular integrals (dpeaa)DE-He213 Bilinear operators (dpeaa)DE-He213 Maximal operators (dpeaa)DE-He213 Fourier multipliers (dpeaa)DE-He213 Honzík, Petr (orcid)0000-0001-6545-6461 aut Enthalten in Collectanea mathematica Barcelona, 1948 70(2019), 3 vom: 31. Jan., Seite 431-446 (DE-627)327535180 (DE-600)2044536-2 2038-4815 nnns volume:70 year:2019 number:3 day:31 month:01 pages:431-446 https://dx.doi.org/10.1007/s13348-019-00239-4 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 70 2019 3 31 01 431-446
allfields_unstemmed	10.1007/s13348-019-00239-4 doi (DE-627)SPR031420079 (SPR)s13348-019-00239-4-e DE-627 ger DE-627 rakwb eng Buriánková, Eva verfasserin (orcid)0000-0002-3491-0761 aut Rough maximal bilinear singular integrals 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Universitat de Barcelona 2019 Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/\|(y,z)\|)\|(y,z)\|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left\| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/\|(y,z)\|)}{ \|(y,z)\|^{2n}}f(x-y)g(x-z) dydz\right\| , \end{aligned}%$where %$\varOmega %$ is a function in %$L^\infty (\mathbb S^{2n-1})%$ with vanishing integral. We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$. Singular integrals (dpeaa)DE-He213 Bilinear operators (dpeaa)DE-He213 Maximal operators (dpeaa)DE-He213 Fourier multipliers (dpeaa)DE-He213 Honzík, Petr (orcid)0000-0001-6545-6461 aut Enthalten in Collectanea mathematica Barcelona, 1948 70(2019), 3 vom: 31. Jan., Seite 431-446 (DE-627)327535180 (DE-600)2044536-2 2038-4815 nnns volume:70 year:2019 number:3 day:31 month:01 pages:431-446 https://dx.doi.org/10.1007/s13348-019-00239-4 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 70 2019 3 31 01 431-446
allfieldsGer	10.1007/s13348-019-00239-4 doi (DE-627)SPR031420079 (SPR)s13348-019-00239-4-e DE-627 ger DE-627 rakwb eng Buriánková, Eva verfasserin (orcid)0000-0002-3491-0761 aut Rough maximal bilinear singular integrals 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Universitat de Barcelona 2019 Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/\|(y,z)\|)\|(y,z)\|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left\| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/\|(y,z)\|)}{ \|(y,z)\|^{2n}}f(x-y)g(x-z) dydz\right\| , \end{aligned}%$where %$\varOmega %$ is a function in %$L^\infty (\mathbb S^{2n-1})%$ with vanishing integral. We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$. Singular integrals (dpeaa)DE-He213 Bilinear operators (dpeaa)DE-He213 Maximal operators (dpeaa)DE-He213 Fourier multipliers (dpeaa)DE-He213 Honzík, Petr (orcid)0000-0001-6545-6461 aut Enthalten in Collectanea mathematica Barcelona, 1948 70(2019), 3 vom: 31. Jan., Seite 431-446 (DE-627)327535180 (DE-600)2044536-2 2038-4815 nnns volume:70 year:2019 number:3 day:31 month:01 pages:431-446 https://dx.doi.org/10.1007/s13348-019-00239-4 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 70 2019 3 31 01 431-446
allfieldsSound	10.1007/s13348-019-00239-4 doi (DE-627)SPR031420079 (SPR)s13348-019-00239-4-e DE-627 ger DE-627 rakwb eng Buriánková, Eva verfasserin (orcid)0000-0002-3491-0761 aut Rough maximal bilinear singular integrals 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Universitat de Barcelona 2019 Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/\|(y,z)\|)\|(y,z)\|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left\| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/\|(y,z)\|)}{ \|(y,z)\|^{2n}}f(x-y)g(x-z) dydz\right\| , \end{aligned}%$where %$\varOmega %$ is a function in %$L^\infty (\mathbb S^{2n-1})%$ with vanishing integral. We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$. Singular integrals (dpeaa)DE-He213 Bilinear operators (dpeaa)DE-He213 Maximal operators (dpeaa)DE-He213 Fourier multipliers (dpeaa)DE-He213 Honzík, Petr (orcid)0000-0001-6545-6461 aut Enthalten in Collectanea mathematica Barcelona, 1948 70(2019), 3 vom: 31. Jan., Seite 431-446 (DE-627)327535180 (DE-600)2044536-2 2038-4815 nnns volume:70 year:2019 number:3 day:31 month:01 pages:431-446 https://dx.doi.org/10.1007/s13348-019-00239-4 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 70 2019 3 31 01 431-446
language	English
source	Enthalten in Collectanea mathematica 70(2019), 3 vom: 31. Jan., Seite 431-446 volume:70 year:2019 number:3 day:31 month:01 pages:431-446
sourceStr	Enthalten in Collectanea mathematica 70(2019), 3 vom: 31. Jan., Seite 431-446 volume:70 year:2019 number:3 day:31 month:01 pages:431-446
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Singular integrals Bilinear operators Maximal operators Fourier multipliers
isfreeaccess_bool	false
container_title	Collectanea mathematica
authorswithroles_txt_mv	Buriánková, Eva @@aut@@ Honzík, Petr @@aut@@
publishDateDaySort_date	2019-01-31T00:00:00Z
hierarchy_top_id	327535180
id	SPR031420079
language_de	englisch
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We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Singular integrals</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bilinear operators</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Maximal operators</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fourier multipliers</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Honzík, Petr</subfield><subfield code="0">(orcid)0000-0001-6545-6461</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Collectanea mathematica</subfield><subfield code="d">Barcelona, 1948</subfield><subfield code="g">70(2019), 3 vom: 31. 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author	Buriánková, Eva
spellingShingle	Buriánková, Eva misc Singular integrals misc Bilinear operators misc Maximal operators misc Fourier multipliers Rough maximal bilinear singular integrals
authorStr	Buriánková, Eva
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topic_title	Rough maximal bilinear singular integrals Singular integrals (dpeaa)DE-He213 Bilinear operators (dpeaa)DE-He213 Maximal operators (dpeaa)DE-He213 Fourier multipliers (dpeaa)DE-He213
topic	misc Singular integrals misc Bilinear operators misc Maximal operators misc Fourier multipliers
topic_unstemmed	misc Singular integrals misc Bilinear operators misc Maximal operators misc Fourier multipliers
topic_browse	misc Singular integrals misc Bilinear operators misc Maximal operators misc Fourier multipliers
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Rough maximal bilinear singular integrals
ctrlnum	(DE-627)SPR031420079 (SPR)s13348-019-00239-4-e
title_full	Rough maximal bilinear singular integrals
author_sort	Buriánková, Eva
journal	Collectanea mathematica
journalStr	Collectanea mathematica
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author_browse	Buriánková, Eva Honzík, Petr
container_volume	70
format_se	Elektronische Aufsätze
author-letter	Buriánková, Eva
doi_str_mv	10.1007/s13348-019-00239-4
normlink	(ORCID)0000-0002-3491-0761 (ORCID)0000-0001-6545-6461
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title_sort	rough maximal bilinear singular integrals
title_auth	Rough maximal bilinear singular integrals
abstract	Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/\|(y,z)\|)\|(y,z)\|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left\| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/\|(y,z)\|)}{ \|(y,z)\|^{2n}}f(x-y)g(x-z) dydz\right\| , \end{aligned}%$where %$\varOmega %$ is a function in %$L^\infty (\mathbb S^{2n-1})%$ with vanishing integral. We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$. © Universitat de Barcelona 2019
abstractGer	Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/\|(y,z)\|)\|(y,z)\|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left\| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/\|(y,z)\|)}{ \|(y,z)\|^{2n}}f(x-y)g(x-z) dydz\right\| , \end{aligned}%$where %$\varOmega %$ is a function in %$L^\infty (\mathbb S^{2n-1})%$ with vanishing integral. We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$. © Universitat de Barcelona 2019
abstract_unstemmed	Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/\|(y,z)\|)\|(y,z)\|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left\| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/\|(y,z)\|)}{ \|(y,z)\|^{2n}}f(x-y)g(x-z) dydz\right\| , \end{aligned}%$where %$\varOmega %$ is a function in %$L^\infty (\mathbb S^{2n-1})%$ with vanishing integral. We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$. © Universitat de Barcelona 2019
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container_issue	3
title_short	Rough maximal bilinear singular integrals
url	https://dx.doi.org/10.1007/s13348-019-00239-4
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author2	Honzík, Petr
author2Str	Honzík, Petr
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doi_str	10.1007/s13348-019-00239-4
up_date	2024-07-03T23:38:03.508Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR031420079</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230331072436.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2019 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s13348-019-00239-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR031420079</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s13348-019-00239-4-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">Buriánková, Eva</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-3491-0761</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Rough maximal bilinear singular integrals</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</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">© Universitat de Barcelona 2019</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We study the rough maximal bilinear singular integral TΩ∗(f,g)(x)=supε>0∫Rn\B0,ε∫Rn\B0,εΩ((y,z)/\|(y,z)\|)\|(y,z)\|2nf(x-y)g(x-z)dydz,%$\begin{aligned} T^{*}_\varOmega (f,g)(x)=\! \sup _{\varepsilon >0}\left\| \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\! \int _{\mathbb {R}^{n}\setminus B\left( 0,\varepsilon \right) }\!\frac{ \varOmega ((y,z)/\|(y,z)\|)}{ \|(y,z)\|^{2n}}f(x-y)g(x-z) dydz\right\| , \end{aligned}%$where %$\varOmega %$ is a function in %$L^\infty (\mathbb S^{2n-1})%$ with vanishing integral. We prove it is bounded from %$L^p\times L^q\rightarrow L^r,%$ where %$1<p,q<\infty %$ and %$1/r=1/p+1/q.%$ We also discuss results for %$\varOmega \in L^s(\mathbb S^{2n-1}),%%%$1<s<\infty %$.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Singular integrals</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bilinear operators</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Maximal operators</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fourier multipliers</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Honzík, Petr</subfield><subfield code="0">(orcid)0000-0001-6545-6461</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Collectanea mathematica</subfield><subfield code="d">Barcelona, 1948</subfield><subfield code="g">70(2019), 3 vom: 31. 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