Muckenhoupt type weights and Berezin formulas for Bergman spaces

By means of Muckenhoupt type conditions, we characterize the weights $\omega$ on $\C$ such that the Bergman projection of $F^{2,\ell}_{\alpha}=H(\C)\cap L^2(\C,e^{-\frac{\alpha}2|z|^{2\ell}})$, $\alpha>0$, $\ell>1$, is bounded on $L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}}\omega(z))$, for $1<p...

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Autores: Cascante, Ma. Carme (Maria Carme), Fàbrega Casamitjana, Joan, Pascuas Tijero, Daniel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
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:2445/184095
Acceso en línea:https://hdl.handle.net/2445/184095
Access Level:acceso abierto
Palabra clave:Representacions integrals
Nuclis de Bergman
Operadors de Toeplitz
Integral representations
Bergman kernel functions
Toeplitz operators
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spelling Muckenhoupt type weights and Berezin formulas for Bergman spacesCascante, Ma. Carme (Maria Carme)Fàbrega Casamitjana, JoanPascuas Tijero, DanielRepresentacions integralsNuclis de BergmanOperadors de ToeplitzIntegral representationsBergman kernel functionsToeplitz operatorsBy means of Muckenhoupt type conditions, we characterize the weights $\omega$ on $\C$ such that the Bergman projection of $F^{2,\ell}_{\alpha}=H(\C)\cap L^2(\C,e^{-\frac{\alpha}2|z|^{2\ell}})$, $\alpha>0$, $\ell>1$, is bounded on $L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}}\omega(z))$, for $1<p<\infty$. We also obtain explicit representation integral formulas for functions in the weighted Bergman spaces $A^p(\omega)=H(\C)\cap L^p(\omega)$. Finally, we check the validity of the so called Sarason conjecture about the boundedness of products of certain Toeplitz operators on the spaces $F^{p,\ell}_\alpha=H(\C)\cap L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}})$.Elsevier2022202220212022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/184095Articles 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/10.1016/j.jmaa.2021.125481Journal of Mathematical Analysis and Applications, 2021, vol. 504, p. 125481https://doi.org/10.1016/j.jmaa.2021.125481cc-by-nc-nd (c) Cascante, C et al., 2021https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/1840952026-05-29T05:05:01Z
dc.title.none.fl_str_mv Muckenhoupt type weights and Berezin formulas for Bergman spaces
title Muckenhoupt type weights and Berezin formulas for Bergman spaces
spellingShingle Muckenhoupt type weights and Berezin formulas for Bergman spaces
Cascante, Ma. Carme (Maria Carme)
Representacions integrals
Nuclis de Bergman
Operadors de Toeplitz
Integral representations
Bergman kernel functions
Toeplitz operators
title_short Muckenhoupt type weights and Berezin formulas for Bergman spaces
title_full Muckenhoupt type weights and Berezin formulas for Bergman spaces
title_fullStr Muckenhoupt type weights and Berezin formulas for Bergman spaces
title_full_unstemmed Muckenhoupt type weights and Berezin formulas for Bergman spaces
title_sort Muckenhoupt type weights and Berezin formulas for Bergman spaces
dc.creator.none.fl_str_mv Cascante, Ma. Carme (Maria Carme)
Fàbrega Casamitjana, Joan
Pascuas Tijero, Daniel
author Cascante, Ma. Carme (Maria Carme)
author_facet Cascante, Ma. Carme (Maria Carme)
Fàbrega Casamitjana, Joan
Pascuas Tijero, Daniel
author_role author
author2 Fàbrega Casamitjana, Joan
Pascuas Tijero, Daniel
author2_role author
author
dc.subject.none.fl_str_mv Representacions integrals
Nuclis de Bergman
Operadors de Toeplitz
Integral representations
Bergman kernel functions
Toeplitz operators
topic Representacions integrals
Nuclis de Bergman
Operadors de Toeplitz
Integral representations
Bergman kernel functions
Toeplitz operators
description By means of Muckenhoupt type conditions, we characterize the weights $\omega$ on $\C$ such that the Bergman projection of $F^{2,\ell}_{\alpha}=H(\C)\cap L^2(\C,e^{-\frac{\alpha}2|z|^{2\ell}})$, $\alpha>0$, $\ell>1$, is bounded on $L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}}\omega(z))$, for $1<p<\infty$. We also obtain explicit representation integral formulas for functions in the weighted Bergman spaces $A^p(\omega)=H(\C)\cap L^p(\omega)$. Finally, we check the validity of the so called Sarason conjecture about the boundedness of products of certain Toeplitz operators on the spaces $F^{p,\ell}_\alpha=H(\C)\cap L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}})$.
publishDate 2021
dc.date.none.fl_str_mv 2021
2022
2022
2022
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/2445/184095
url https://hdl.handle.net/2445/184095
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/10.1016/j.jmaa.2021.125481
Journal of Mathematical Analysis and Applications, 2021, vol. 504, p. 125481
https://doi.org/10.1016/j.jmaa.2021.125481
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Cascante, C et al., 2021
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Cascante, C et al., 2021
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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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