Two-weight, weak-type norm inequalities for singular integral operators

We give a sufficient condition for singular integral operators and, more generally, Calder´on-Zygmund operators to satisfy the weak (p, p) inequality u({x ∈ R n : |T f(x)| > t}) ≤ C / tp Z Rn |f|p v dx, 1 < p < ∞. Our condition is an Ap-type condition in the scale of Orlicz spaces: kukL(log...

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Detalles Bibliográficos
Autores: Cruz Uribe, David, Pérez Moreno, Carlos
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:1999
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/48500
Acceso en línea:http://hdl.handle.net/11441/48500
https://doi.org/10.4310/MRL.1999.v6.n4.a4
Access Level:acceso abierto
Palabra clave:Weights
Singular integral operators
Calderón-Zygmund operators
Maximal operators
Orlicz spaces
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spelling Two-weight, weak-type norm inequalities for singular integral operatorsCruz Uribe, DavidPérez Moreno, CarlosWeightsSingular integral operatorsCalderón-Zygmund operatorsMaximal operatorsOrlicz spacesWe give a sufficient condition for singular integral operators and, more generally, Calder´on-Zygmund operators to satisfy the weak (p, p) inequality u({x ∈ R n : |T f(x)| > t}) ≤ C / tp Z Rn |f|p v dx, 1 < p < ∞. Our condition is an Ap-type condition in the scale of Orlicz spaces: kukL(log L) p−1+δ,Q 1 |Q| Z Q v −p 0/p dx p/p0 ≤ K < ∞, δ > 0. This conditions is stronger than the Ap condition and is sharp since it fails when δ = 0.Dirección General de Investigación Científica y TécnicaInternational PressAnálisis MatemáticoFQM354: Análisis RealDirección General de Investigación Científica y Técnica (DGICYT). España1999info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/48500https://doi.org/10.4310/MRL.1999.v6.n4.a4reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMathematical Research Letters, 6 (4), 417-427.PB40192http://intlpress.com/site/pub/files/_fulltext/journals/mrl/1999/0006/0004/MRL-1999-0006-0004-a004.pdfinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/485002026-06-17T12:51:07Z
dc.title.none.fl_str_mv Two-weight, weak-type norm inequalities for singular integral operators
title Two-weight, weak-type norm inequalities for singular integral operators
spellingShingle Two-weight, weak-type norm inequalities for singular integral operators
Cruz Uribe, David
Weights
Singular integral operators
Calderón-Zygmund operators
Maximal operators
Orlicz spaces
title_short Two-weight, weak-type norm inequalities for singular integral operators
title_full Two-weight, weak-type norm inequalities for singular integral operators
title_fullStr Two-weight, weak-type norm inequalities for singular integral operators
title_full_unstemmed Two-weight, weak-type norm inequalities for singular integral operators
title_sort Two-weight, weak-type norm inequalities for singular integral operators
dc.creator.none.fl_str_mv Cruz Uribe, David
Pérez Moreno, Carlos
author Cruz Uribe, David
author_facet Cruz Uribe, David
Pérez Moreno, Carlos
author_role author
author2 Pérez Moreno, Carlos
author2_role author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM354: Análisis Real
Dirección General de Investigación Científica y Técnica (DGICYT). España
dc.subject.none.fl_str_mv Weights
Singular integral operators
Calderón-Zygmund operators
Maximal operators
Orlicz spaces
topic Weights
Singular integral operators
Calderón-Zygmund operators
Maximal operators
Orlicz spaces
description We give a sufficient condition for singular integral operators and, more generally, Calder´on-Zygmund operators to satisfy the weak (p, p) inequality u({x ∈ R n : |T f(x)| > t}) ≤ C / tp Z Rn |f|p v dx, 1 < p < ∞. Our condition is an Ap-type condition in the scale of Orlicz spaces: kukL(log L) p−1+δ,Q 1 |Q| Z Q v −p 0/p dx p/p0 ≤ K < ∞, δ > 0. This conditions is stronger than the Ap condition and is sharp since it fails when δ = 0.
publishDate 1999
dc.date.none.fl_str_mv 1999
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/48500
https://doi.org/10.4310/MRL.1999.v6.n4.a4
url http://hdl.handle.net/11441/48500
https://doi.org/10.4310/MRL.1999.v6.n4.a4
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematical Research Letters, 6 (4), 417-427.
PB40192
http://intlpress.com/site/pub/files/_fulltext/journals/mrl/1999/0006/0004/MRL-1999-0006-0004-a004.pdf
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 International Press
publisher.none.fl_str_mv International Press
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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