Mixed estimates for singular integrals on weighted Hardy spaces

In this paper we give quantitative bounds for the norms of different kinds of singular integral operators on weighted Hardy spaces H<sup>p</sup><sub>w</sub>, where 0 < p ≤ 1 and w is a weight in the Muckenhoupt A<sub>∞</sub> class. We deal with Fourier multipli...

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Detalles Bibliográficos
Autores: Cejas, María Eugenia, Dalmasso, Estefanía
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:Argentina
Institución:Universidad Nacional de La Plata
Repositorio:SEDICI (UNLP)
Idioma:inglés
OAI Identifier:oai:sedici.unlp.edu.ar:10915/131013
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/131013
Access Level:acceso abierto
Palabra clave:Ciencias Exactas
Weighted Hardy spaces
Singular integrals
Mixed estimates
Calderón–Zygmund operators
Fourier multipliers
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spelling Mixed estimates for singular integrals on weighted Hardy spacesCejas, María EugeniaDalmasso, EstefaníaCiencias ExactasWeighted Hardy spacesSingular integralsMixed estimatesCalderón–Zygmund operatorsFourier multipliersIn this paper we give quantitative bounds for the norms of different kinds of singular integral operators on weighted Hardy spaces H<sup>p</sup><sub>w</sub>, where 0 < p ≤ 1 and w is a weight in the Muckenhoupt A<sub>∞</sub> class. We deal with Fourier multiplier operators, Calderon–Zygmund operators of homogeneous type which are particular cases of the first ones, and, more generally, we study singular integrals of convolution type. In order to prove mixed estimates in the setting of weighted Hardy spaces, we need to introduce several characterizations of weighted Hardy spaces by means of square functions, Littlewood–Paley functions and the grand maximal function. We also establish explicit quantitative bounds depending on the weight w when switching between the H<sup>p</sup><sub>w</sub>-norms defined by the Littlewood–Paley–Stein square function and its discrete version, and also by applying the mixed bound A<sub>q</sub>–A<sub>∞</sub> result for the vector-valued extension of the Hardy–Littlewood maximal operator given in Buckley (Trans Am Math Soc 340(1):253–272, 1993).Facultad de Ciencias Exactas2020-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf745-766http://sedici.unlp.edu.ar/handle/10915/131013enginfo:eu-repo/semantics/altIdentifier/issn/1139-1138info:eu-repo/semantics/altIdentifier/issn/1988-2807info:eu-repo/semantics/altIdentifier/doi/10.1007/s13163-019-00331-0info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2024-05-08T13:10:08Zoai:sedici.unlp.edu.ar:10915/131013Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292024-05-08 13:10:09.21SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Mixed estimates for singular integrals on weighted Hardy spaces
title Mixed estimates for singular integrals on weighted Hardy spaces
spellingShingle Mixed estimates for singular integrals on weighted Hardy spaces
Cejas, María Eugenia
Ciencias Exactas
Weighted Hardy spaces
Singular integrals
Mixed estimates
Calderón–Zygmund operators
Fourier multipliers
title_short Mixed estimates for singular integrals on weighted Hardy spaces
title_full Mixed estimates for singular integrals on weighted Hardy spaces
title_fullStr Mixed estimates for singular integrals on weighted Hardy spaces
title_full_unstemmed Mixed estimates for singular integrals on weighted Hardy spaces
title_sort Mixed estimates for singular integrals on weighted Hardy spaces
dc.creator.none.fl_str_mv Cejas, María Eugenia
Dalmasso, Estefanía
author Cejas, María Eugenia
author_facet Cejas, María Eugenia
Dalmasso, Estefanía
author_role author
author2 Dalmasso, Estefanía
author2_role author
dc.subject.none.fl_str_mv Ciencias Exactas
Weighted Hardy spaces
Singular integrals
Mixed estimates
Calderón–Zygmund operators
Fourier multipliers
topic Ciencias Exactas
Weighted Hardy spaces
Singular integrals
Mixed estimates
Calderón–Zygmund operators
Fourier multipliers
description In this paper we give quantitative bounds for the norms of different kinds of singular integral operators on weighted Hardy spaces H<sup>p</sup><sub>w</sub>, where 0 < p ≤ 1 and w is a weight in the Muckenhoupt A<sub>∞</sub> class. We deal with Fourier multiplier operators, Calderon–Zygmund operators of homogeneous type which are particular cases of the first ones, and, more generally, we study singular integrals of convolution type. In order to prove mixed estimates in the setting of weighted Hardy spaces, we need to introduce several characterizations of weighted Hardy spaces by means of square functions, Littlewood–Paley functions and the grand maximal function. We also establish explicit quantitative bounds depending on the weight w when switching between the H<sup>p</sup><sub>w</sub>-norms defined by the Littlewood–Paley–Stein square function and its discrete version, and also by applying the mixed bound A<sub>q</sub>–A<sub>∞</sub> result for the vector-valued extension of the Hardy–Littlewood maximal operator given in Buckley (Trans Am Math Soc 340(1):253–272, 1993).
publishDate 2020
dc.date.none.fl_str_mv 2020-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/131013
url http://sedici.unlp.edu.ar/handle/10915/131013
dc.language.none.fl_str_mv eng
language eng
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info:eu-repo/semantics/altIdentifier/issn/1988-2807
info:eu-repo/semantics/altIdentifier/doi/10.1007/s13163-019-00331-0
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
745-766
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
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instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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