Borderline weighted estimates for commutators of singular integrals

In this paper we establish the following estimate w({x∈Rn:|[b,T]f(x)|>λ})≤cTε2∫RnΦ(∥b∥BMO|f(x)|λ)ML(logL)1+εw(x)dx where w≥0,0<ε<1 and Φ(t)=t(t+log+(t)). This inequality relies upon the following sharp Lp estimate ∥[b,T]f∥Lp(w)≤cT(p′)2p2(p−1δ)1p′∥b∥BMO∥f∥Lp(ML(logL)2p−1+δw) where 1<p<...

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Detalles Bibliográficos
Autores: Pérez Moreno, Carlos, Rivera Ríos, Israel Pablo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42872
Acceso en línea:http://hdl.handle.net/11441/42872
Access Level:acceso abierto
Palabra clave:commutators
Rubio de Francia extrapolation
Ap weights
Hardy-Littlewood maximal function
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repository_id_str
spelling Borderline weighted estimates for commutators of singular integralsPérez Moreno, CarlosRivera Ríos, Israel PablocommutatorsRubio de Francia extrapolationAp weightsHardy-Littlewood maximal functionIn this paper we establish the following estimate w({x∈Rn:|[b,T]f(x)|>λ})≤cTε2∫RnΦ(∥b∥BMO|f(x)|λ)ML(logL)1+εw(x)dx where w≥0,0<ε<1 and Φ(t)=t(t+log+(t)). This inequality relies upon the following sharp Lp estimate ∥[b,T]f∥Lp(w)≤cT(p′)2p2(p−1δ)1p′∥b∥BMO∥f∥Lp(ML(logL)2p−1+δw) where 1<p<∞,w≥0 and 0<δ<1. As a consequence we recover the following estimate w({x∈Rn:|[b,T]f(x)|>λ})≤cT[w]A∞(1+log+[w]A∞)2∫RnΦ(∥b∥BMO|f(x)|λ)Mw(x)dx We also obtain the analogue estimates for symbol-multilinear commutators for a wider class of symbols.Ministerio de Economía y CompetitividadSpringerAnálisis MatemáticoFQM-354 Análisis RealMinisterio de Economía y Competitividad (MINECO). España2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/42872reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésIsrael Journal of Mathematicsinfo:eu-repo/grantAgreement/MINECO/MTM2014-53850-P/info:eu-repo/grantAgreement/MINECO/MTM2012-30748/info:eu-repo/semantics/openAccessoai:idus.us.es:11441/428722026-06-17T12:51:07Z
dc.title.none.fl_str_mv Borderline weighted estimates for commutators of singular integrals
title Borderline weighted estimates for commutators of singular integrals
spellingShingle Borderline weighted estimates for commutators of singular integrals
Pérez Moreno, Carlos
commutators
Rubio de Francia extrapolation
Ap weights
Hardy-Littlewood maximal function
title_short Borderline weighted estimates for commutators of singular integrals
title_full Borderline weighted estimates for commutators of singular integrals
title_fullStr Borderline weighted estimates for commutators of singular integrals
title_full_unstemmed Borderline weighted estimates for commutators of singular integrals
title_sort Borderline weighted estimates for commutators of singular integrals
dc.creator.none.fl_str_mv Pérez Moreno, Carlos
Rivera Ríos, Israel Pablo
author Pérez Moreno, Carlos
author_facet Pérez Moreno, Carlos
Rivera Ríos, Israel Pablo
author_role author
author2 Rivera Ríos, Israel Pablo
author2_role author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM-354 Análisis Real
Ministerio de Economía y Competitividad (MINECO). España
dc.subject.none.fl_str_mv commutators
Rubio de Francia extrapolation
Ap weights
Hardy-Littlewood maximal function
topic commutators
Rubio de Francia extrapolation
Ap weights
Hardy-Littlewood maximal function
description In this paper we establish the following estimate w({x∈Rn:|[b,T]f(x)|>λ})≤cTε2∫RnΦ(∥b∥BMO|f(x)|λ)ML(logL)1+εw(x)dx where w≥0,0<ε<1 and Φ(t)=t(t+log+(t)). This inequality relies upon the following sharp Lp estimate ∥[b,T]f∥Lp(w)≤cT(p′)2p2(p−1δ)1p′∥b∥BMO∥f∥Lp(ML(logL)2p−1+δw) where 1<p<∞,w≥0 and 0<δ<1. As a consequence we recover the following estimate w({x∈Rn:|[b,T]f(x)|>λ})≤cT[w]A∞(1+log+[w]A∞)2∫RnΦ(∥b∥BMO|f(x)|λ)Mw(x)dx We also obtain the analogue estimates for symbol-multilinear commutators for a wider class of symbols.
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/42872
url http://hdl.handle.net/11441/42872
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Israel Journal of Mathematics
info:eu-repo/grantAgreement/MINECO/MTM2014-53850-P/
info:eu-repo/grantAgreement/MINECO/MTM2012-30748/
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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