The precise representative for the gradient of the Riesz potential of a finite measure

Given a finite nonnegative Borel measure (Formula presented.) in (Formula presented.), we identify the Lebesgue set (Formula presented.) of the vector-valued function (Formula presented.) for any order (Formula presented.). We prove that (Formula presented.) if and only if the integral above has a p...

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Detalles Bibliográficos
Autores: Cufí, J., Ponce, A.C., Verdera, J.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/531783
Acceso en línea:http://hdl.handle.net/2072/531783
Access Level:acceso abierto
Palabra clave:Matemàtiques, " Riesz potential"
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spelling The precise representative for the gradient of the Riesz potential of a finite measureCufí, J.Ponce, A.C.Verdera, J.Matemàtiques, " Riesz potential"Given a finite nonnegative Borel measure (Formula presented.) in (Formula presented.), we identify the Lebesgue set (Formula presented.) of the vector-valued function (Formula presented.) for any order (Formula presented.). We prove that (Formula presented.) if and only if the integral above has a principal value at (Formula presented.) and (Formula presented.) In that case, the precise representative of (Formula presented.) at (Formula presented.) coincides with the principal value of the integral. We also study the existence of Lebesgue points for the Cauchy integral of the intrinsic probability measure associated with planar Cantor sets, which leads to challenging new questions. © 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.This work also acknowledges the CERCA Programme of the Generalitat de Catalunya for institutional support. This work was also supported by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centres and Units of Excellence in R&D (CEX2020-001084-M).John Wiley and Sons Ltd2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion20 p.application/pdfhttp://hdl.handle.net/2072/531783RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésJournal of the London Mathematical Societyinfo:eu-repo/semantics/openAccessoai:recercat.cat:2072/5317832026-05-29T05:05:01Z
dc.title.none.fl_str_mv The precise representative for the gradient of the Riesz potential of a finite measure
title The precise representative for the gradient of the Riesz potential of a finite measure
spellingShingle The precise representative for the gradient of the Riesz potential of a finite measure
Cufí, J.
Matemàtiques, " Riesz potential"
title_short The precise representative for the gradient of the Riesz potential of a finite measure
title_full The precise representative for the gradient of the Riesz potential of a finite measure
title_fullStr The precise representative for the gradient of the Riesz potential of a finite measure
title_full_unstemmed The precise representative for the gradient of the Riesz potential of a finite measure
title_sort The precise representative for the gradient of the Riesz potential of a finite measure
dc.creator.none.fl_str_mv Cufí, J.
Ponce, A.C.
Verdera, J.
author Cufí, J.
author_facet Cufí, J.
Ponce, A.C.
Verdera, J.
author_role author
author2 Ponce, A.C.
Verdera, J.
author2_role author
author
dc.subject.none.fl_str_mv Matemàtiques, " Riesz potential"
topic Matemàtiques, " Riesz potential"
description Given a finite nonnegative Borel measure (Formula presented.) in (Formula presented.), we identify the Lebesgue set (Formula presented.) of the vector-valued function (Formula presented.) for any order (Formula presented.). We prove that (Formula presented.) if and only if the integral above has a principal value at (Formula presented.) and (Formula presented.) In that case, the precise representative of (Formula presented.) at (Formula presented.) coincides with the principal value of the integral. We also study the existence of Lebesgue points for the Cauchy integral of the intrinsic probability measure associated with planar Cantor sets, which leads to challenging new questions. © 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
publishDate 2022
dc.date.none.fl_str_mv 2022
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/2072/531783
url http://hdl.handle.net/2072/531783
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of the London Mathematical Society
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 20 p.
application/pdf
dc.publisher.none.fl_str_mv John Wiley and Sons Ltd
publisher.none.fl_str_mv John Wiley and Sons Ltd
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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