Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.

Abstract. We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimet- ric inequality and of Weissler's inequality for dilations. By contractivity and a standard tensorization procedure, the unit disc in...

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Autores: Bayart, Frédéric, Brevig, Ole Fredrik, Haimi, Antti, Ortega Cerdà, Joaquim, Perfekt, Karl-Mikael
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Recursos: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:2445/127239
Acesso em linha:https://hdl.handle.net/2445/127239
Access Level:acceso abierto
Palavra-chave:Funcions de variables complexes
Àlgebres de funcions
Funcions analítiques
Operadors lineals
Teoria d'operadors
Functions of complex variables
Function algebras
Analytic functions
Linear operators
Operator theory
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spelling Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.Bayart, FrédéricBrevig, Ole FredrikHaimi, AnttiOrtega Cerdà, JoaquimPerfekt, Karl-MikaelFuncions de variables complexesÀlgebres de funcionsFuncions analítiquesOperadors linealsTeoria d'operadorsFunctions of complex variablesFunction algebrasAnalytic functionsLinear operatorsOperator theoryAbstract. We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimet- ric inequality and of Weissler's inequality for dilations. By contractivity and a standard tensorization procedure, the unit disc inequalities yield correspond- ing inequalities for the Bergman spaces of Dirichlet series. We use these results to study weighted multiplicative Hankel forms associated with the Bergman spaces of Dirichlet series, reproducing most of the known results on multi- plicative Hankel forms associated with the Hardy spaces of Dirichlet series. In addition, we find a direct relationship between the two types of forms which does not exist in lower dimensions. Finally, we produce some counterexamples concerning Carleson measures on the infinite polydisc.American Mathematical Society (AMS)2019201920192019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion27 p.application/pdfhttps://hdl.handle.net/2445/127239Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: https://doi.org/10.1090/tran/7290Transactions of the American Mathematical Society, 2019, vol. 371, num. 1, p. 681-707https://doi.org/10.1090/tran/7290cc-by-nc-nd (c) American Mathematical Society (AMS), 2019http://creativecommons.org/licenses/by-nc-nd/3.0/esinfo:eu-repo/semantics/openAccessoai:recercat.cat:2445/1272392026-05-29T05:05:01Z
dc.title.none.fl_str_mv Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.
title Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.
spellingShingle Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.
Bayart, Frédéric
Funcions de variables complexes
Àlgebres de funcions
Funcions analítiques
Operadors lineals
Teoria d'operadors
Functions of complex variables
Function algebras
Analytic functions
Linear operators
Operator theory
title_short Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.
title_full Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.
title_fullStr Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.
title_full_unstemmed Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.
title_sort Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.
dc.creator.none.fl_str_mv Bayart, Frédéric
Brevig, Ole Fredrik
Haimi, Antti
Ortega Cerdà, Joaquim
Perfekt, Karl-Mikael
author Bayart, Frédéric
author_facet Bayart, Frédéric
Brevig, Ole Fredrik
Haimi, Antti
Ortega Cerdà, Joaquim
Perfekt, Karl-Mikael
author_role author
author2 Brevig, Ole Fredrik
Haimi, Antti
Ortega Cerdà, Joaquim
Perfekt, Karl-Mikael
author2_role author
author
author
author
dc.subject.none.fl_str_mv Funcions de variables complexes
Àlgebres de funcions
Funcions analítiques
Operadors lineals
Teoria d'operadors
Functions of complex variables
Function algebras
Analytic functions
Linear operators
Operator theory
topic Funcions de variables complexes
Àlgebres de funcions
Funcions analítiques
Operadors lineals
Teoria d'operadors
Functions of complex variables
Function algebras
Analytic functions
Linear operators
Operator theory
description Abstract. We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimet- ric inequality and of Weissler's inequality for dilations. By contractivity and a standard tensorization procedure, the unit disc inequalities yield correspond- ing inequalities for the Bergman spaces of Dirichlet series. We use these results to study weighted multiplicative Hankel forms associated with the Bergman spaces of Dirichlet series, reproducing most of the known results on multi- plicative Hankel forms associated with the Hardy spaces of Dirichlet series. In addition, we find a direct relationship between the two types of forms which does not exist in lower dimensions. Finally, we produce some counterexamples concerning Carleson measures on the infinite polydisc.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019
2019
2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/127239
url https://hdl.handle.net/2445/127239
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1090/tran/7290
Transactions of the American Mathematical Society, 2019, vol. 371, num. 1, p. 681-707
https://doi.org/10.1090/tran/7290
dc.rights.none.fl_str_mv cc-by-nc-nd (c) American Mathematical Society (AMS), 2019
http://creativecommons.org/licenses/by-nc-nd/3.0/es
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) American Mathematical Society (AMS), 2019
http://creativecommons.org/licenses/by-nc-nd/3.0/es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 27 p.
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society (AMS)
publisher.none.fl_str_mv American Mathematical Society (AMS)
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
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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score 15.81155

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