Sharp weighted estimates for approximating dyadic operators

We give a new proof of the sharp weighted L2 inequality ||T||_{L^2(w)} \leq c [w]_{A_2} where T is the Hilbert transform, a Riesz transform, the Beurling-Ahlfors operator or any operator that can be approximated by Haar shift operators. Our proof avoids the Bellman function technique and two weight...

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Detalhes bibliográficos
Autores: Cruz Uribe, David, Martell Berrocal, José María, Pérez Moreno, Carlos
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2010
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42344
Acesso em linha:http://hdl.handle.net/11441/42344
https://doi.org/10.3934/era.2010.17.12
Access Level:Acceso aberto
Palavra-chave:Ap weights
Haar shift operators singular integral operators
Hilbert transform
Riesz transforms
Beurling-Ahlfors operator
dyadic square function
vector-valued maximal operator
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spelling Sharp weighted estimates for approximating dyadic operatorsCruz Uribe, DavidMartell Berrocal, José MaríaPérez Moreno, CarlosAp weightsHaar shift operators singular integral operatorsHilbert transformRiesz transformsBeurling-Ahlfors operatordyadic square functionvector-valued maximal operatorWe give a new proof of the sharp weighted L2 inequality ||T||_{L^2(w)} \leq c [w]_{A_2} where T is the Hilbert transform, a Riesz transform, the Beurling-Ahlfors operator or any operator that can be approximated by Haar shift operators. Our proof avoids the Bellman function technique and two weight norm inequalities. We use instead a recent result due to A. Lerner to estimate the oscillation of dyadic operators.Faculty Research Committee and the Stewart-Dorwart Faculty Development Fund (Trinity College)Ministerio de Ciencia e InnovaciónConsejo Superior de Investigaciones CientíficasAmerican Mathematical SocietyAnálisis Matemático2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/42344https://doi.org/10.3934/era.2010.17.12reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésElectronic Research Announcements of the American Mathematical Society, 17, 12-19.MTM2009-08934MTM2007-60952PIE 200850I015http://dx.doi.org/10.3934/era.2010.17.12Providence (Rhode Island)info:eu-repo/semantics/openAccessoai:idus.us.es:11441/423442026-06-17T12:51:07Z
dc.title.none.fl_str_mv Sharp weighted estimates for approximating dyadic operators
title Sharp weighted estimates for approximating dyadic operators
spellingShingle Sharp weighted estimates for approximating dyadic operators
Cruz Uribe, David
Ap weights
Haar shift operators singular integral operators
Hilbert transform
Riesz transforms
Beurling-Ahlfors operator
dyadic square function
vector-valued maximal operator
title_short Sharp weighted estimates for approximating dyadic operators
title_full Sharp weighted estimates for approximating dyadic operators
title_fullStr Sharp weighted estimates for approximating dyadic operators
title_full_unstemmed Sharp weighted estimates for approximating dyadic operators
title_sort Sharp weighted estimates for approximating dyadic operators
dc.creator.none.fl_str_mv Cruz Uribe, David
Martell Berrocal, José María
Pérez Moreno, Carlos
author Cruz Uribe, David
author_facet Cruz Uribe, David
Martell Berrocal, José María
Pérez Moreno, Carlos
author_role author
author2 Martell Berrocal, José María
Pérez Moreno, Carlos
author2_role author
author
dc.contributor.none.fl_str_mv Análisis Matemático
dc.subject.none.fl_str_mv Ap weights
Haar shift operators singular integral operators
Hilbert transform
Riesz transforms
Beurling-Ahlfors operator
dyadic square function
vector-valued maximal operator
topic Ap weights
Haar shift operators singular integral operators
Hilbert transform
Riesz transforms
Beurling-Ahlfors operator
dyadic square function
vector-valued maximal operator
description We give a new proof of the sharp weighted L2 inequality ||T||_{L^2(w)} \leq c [w]_{A_2} where T is the Hilbert transform, a Riesz transform, the Beurling-Ahlfors operator or any operator that can be approximated by Haar shift operators. Our proof avoids the Bellman function technique and two weight norm inequalities. We use instead a recent result due to A. Lerner to estimate the oscillation of dyadic operators.
publishDate 2010
dc.date.none.fl_str_mv 2010
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/42344
https://doi.org/10.3934/era.2010.17.12
url http://hdl.handle.net/11441/42344
https://doi.org/10.3934/era.2010.17.12
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Electronic Research Announcements of the American Mathematical Society, 17, 12-19.
MTM2009-08934
MTM2007-60952
PIE 200850I015
http://dx.doi.org/10.3934/era.2010.17.12
Providence (Rhode Island)
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 American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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 15,300719

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