Hausdorff-Young-type inequalities for vector-valued Dirichlet series

Autores
Carando, Daniel Germán; Marceca, Felipe; Sevilla Peris, Pablo
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study Hausdorff-Young-type inequalities for vector-valued Dirichlet series which allow us to compare the norm of a Dirichlet series in the Hardy space Hp(X) with the q-norm of its coefficients. In order to obtain inequalities completely analogous to the scalar case, a Banach space must satisfy the restrictive notion of Fourier type/cotype. We show that variants of these inequalities hold for the much broader range of spaces enjoying type/cotype. We also consider Hausdorff-Young-type inequalities for functions defined on the infinite torus T ∞ or the boolean cube {-1, 1}∞. As a fundamental tool we show that type and cotype are equivalent to a hypercontractive homogeneous polynomial type and cotype, a result of independent interest.
Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Marceca, Felipe. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Sevilla Peris, Pablo. Universidad Politécnica de Valencia; España
Materia
HAUSDORFF-YOUNG INEQUALITIES
DIRICHLET SERIES
BANACH SPACES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/141626
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Hausdorff-Young-type inequalities for vector-valued Dirichlet seriesCarando, Daniel GermánMarceca, FelipeSevilla Peris, PabloHAUSDORFF-YOUNG INEQUALITIESDIRICHLET SERIESBANACH SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study Hausdorff-Young-type inequalities for vector-valued Dirichlet series which allow us to compare the norm of a Dirichlet series in the Hardy space Hp(X) with the q-norm of its coefficients. In order to obtain inequalities completely analogous to the scalar case, a Banach space must satisfy the restrictive notion of Fourier type/cotype. We show that variants of these inequalities hold for the much broader range of spaces enjoying type/cotype. We also consider Hausdorff-Young-type inequalities for functions defined on the infinite torus T ∞ or the boolean cube {-1, 1}∞. As a fundamental tool we show that type and cotype are equivalent to a hypercontractive homogeneous polynomial type and cotype, a result of independent interest.Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Marceca, Felipe. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Sevilla Peris, Pablo. Universidad Politécnica de Valencia; EspañaAmerican Mathematical Society2020-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/141626Carando, Daniel Germán; Marceca, Felipe; Sevilla Peris, Pablo; Hausdorff-Young-type inequalities for vector-valued Dirichlet series; American Mathematical Society; Transactions Of The American Mathematical Society; 373; 8; 8-2020; 5627-56520002-9947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/tran/2020-373-08/S0002-9947-2020-08147-1/info:eu-repo/semantics/altIdentifier/doi/10.1090/tran/8147info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1904.00041info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:21:51Zoai:ri.conicet.gov.ar:11336/141626instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:21:52.091CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Hausdorff-Young-type inequalities for vector-valued Dirichlet series
title Hausdorff-Young-type inequalities for vector-valued Dirichlet series
spellingShingle Hausdorff-Young-type inequalities for vector-valued Dirichlet series
Carando, Daniel Germán
HAUSDORFF-YOUNG INEQUALITIES
DIRICHLET SERIES
BANACH SPACES
title_short Hausdorff-Young-type inequalities for vector-valued Dirichlet series
title_full Hausdorff-Young-type inequalities for vector-valued Dirichlet series
title_fullStr Hausdorff-Young-type inequalities for vector-valued Dirichlet series
title_full_unstemmed Hausdorff-Young-type inequalities for vector-valued Dirichlet series
title_sort Hausdorff-Young-type inequalities for vector-valued Dirichlet series
dc.creator.none.fl_str_mv Carando, Daniel Germán
Marceca, Felipe
Sevilla Peris, Pablo
author Carando, Daniel Germán
author_facet Carando, Daniel Germán
Marceca, Felipe
Sevilla Peris, Pablo
author_role author
author2 Marceca, Felipe
Sevilla Peris, Pablo
author2_role author
author
dc.subject.none.fl_str_mv HAUSDORFF-YOUNG INEQUALITIES
DIRICHLET SERIES
BANACH SPACES
topic HAUSDORFF-YOUNG INEQUALITIES
DIRICHLET SERIES
BANACH SPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study Hausdorff-Young-type inequalities for vector-valued Dirichlet series which allow us to compare the norm of a Dirichlet series in the Hardy space Hp(X) with the q-norm of its coefficients. In order to obtain inequalities completely analogous to the scalar case, a Banach space must satisfy the restrictive notion of Fourier type/cotype. We show that variants of these inequalities hold for the much broader range of spaces enjoying type/cotype. We also consider Hausdorff-Young-type inequalities for functions defined on the infinite torus T ∞ or the boolean cube {-1, 1}∞. As a fundamental tool we show that type and cotype are equivalent to a hypercontractive homogeneous polynomial type and cotype, a result of independent interest.
Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Marceca, Felipe. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Sevilla Peris, Pablo. Universidad Politécnica de Valencia; España
description We study Hausdorff-Young-type inequalities for vector-valued Dirichlet series which allow us to compare the norm of a Dirichlet series in the Hardy space Hp(X) with the q-norm of its coefficients. In order to obtain inequalities completely analogous to the scalar case, a Banach space must satisfy the restrictive notion of Fourier type/cotype. We show that variants of these inequalities hold for the much broader range of spaces enjoying type/cotype. We also consider Hausdorff-Young-type inequalities for functions defined on the infinite torus T ∞ or the boolean cube {-1, 1}∞. As a fundamental tool we show that type and cotype are equivalent to a hypercontractive homogeneous polynomial type and cotype, a result of independent interest.
publishDate 2020
dc.date.none.fl_str_mv 2020-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/141626
Carando, Daniel Germán; Marceca, Felipe; Sevilla Peris, Pablo; Hausdorff-Young-type inequalities for vector-valued Dirichlet series; American Mathematical Society; Transactions Of The American Mathematical Society; 373; 8; 8-2020; 5627-5652
0002-9947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/141626
identifier_str_mv Carando, Daniel Germán; Marceca, Felipe; Sevilla Peris, Pablo; Hausdorff-Young-type inequalities for vector-valued Dirichlet series; American Mathematical Society; Transactions Of The American Mathematical Society; 373; 8; 8-2020; 5627-5652
0002-9947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/tran/2020-373-08/S0002-9947-2020-08147-1/
info:eu-repo/semantics/altIdentifier/doi/10.1090/tran/8147
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1904.00041
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
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:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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