Some revisited results about composition operators on Hardy spaces

We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on HΨ; construction of a surjective symbol whose composition operator is compact on HΨ a...

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Detalles Bibliográficos
Autores: Lefèvre, Pascal, Li, Daniel, Queffélec, Hervé, Rodríguez Piazza, Luis
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2012
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/46376
Acceso en línea:http://hdl.handle.net/11441/46376
https://doi.org/10.4171/RMI/666
Access Level:acceso abierto
Palabra clave:Blaschke product
Carleson function
Carleson measure
Composition operator
Hardy-Orlicz space
Nevanlinna counting function
Schatten classes
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spelling Some revisited results about composition operators on Hardy spacesLefèvre, PascalLi, DanielQueffélec, HervéRodríguez Piazza, LuisBlaschke productCarleson functionCarleson measureComposition operatorHardy-Orlicz spaceNevanlinna counting functionSchatten classesWe generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on HΨ; construction of a surjective symbol whose composition operator is compact on HΨ and, moreover, is in all the Schatten classes Sp(H2), p > 0. On the other hand, we revisit the classical case of composition operators on H2, giving first a new, and simplier, characterization of closed range composition operators, and then showing directly the equivalence of the two characterizations of membership in the Schatten classes of Luecking and Luecking and Zhu.Ministerio de Educación y CienciaEuropean Mathematical SocietyAnálisis MatemáticoFQM104: Analisis MatemáticoMinisterio de Educación y Ciencia (MEC). España2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/46376https://doi.org/10.4171/RMI/666reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésRevista Matemática Iberoamericana, 28 (1), 57-76.MTM2006-05622http://www.ems-ph.org/journals/show_pdf.php?issn=0213-2230&vol=28&iss=1&rank=3info:eu-repo/semantics/openAccessoai:idus.us.es:11441/463762026-06-17T12:51:07Z
dc.title.none.fl_str_mv Some revisited results about composition operators on Hardy spaces
title Some revisited results about composition operators on Hardy spaces
spellingShingle Some revisited results about composition operators on Hardy spaces
Lefèvre, Pascal
Blaschke product
Carleson function
Carleson measure
Composition operator
Hardy-Orlicz space
Nevanlinna counting function
Schatten classes
title_short Some revisited results about composition operators on Hardy spaces
title_full Some revisited results about composition operators on Hardy spaces
title_fullStr Some revisited results about composition operators on Hardy spaces
title_full_unstemmed Some revisited results about composition operators on Hardy spaces
title_sort Some revisited results about composition operators on Hardy spaces
dc.creator.none.fl_str_mv Lefèvre, Pascal
Li, Daniel
Queffélec, Hervé
Rodríguez Piazza, Luis
author Lefèvre, Pascal
author_facet Lefèvre, Pascal
Li, Daniel
Queffélec, Hervé
Rodríguez Piazza, Luis
author_role author
author2 Li, Daniel
Queffélec, Hervé
Rodríguez Piazza, Luis
author2_role author
author
author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM104: Analisis Matemático
Ministerio de Educación y Ciencia (MEC). España
dc.subject.none.fl_str_mv Blaschke product
Carleson function
Carleson measure
Composition operator
Hardy-Orlicz space
Nevanlinna counting function
Schatten classes
topic Blaschke product
Carleson function
Carleson measure
Composition operator
Hardy-Orlicz space
Nevanlinna counting function
Schatten classes
description We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on HΨ; construction of a surjective symbol whose composition operator is compact on HΨ and, moreover, is in all the Schatten classes Sp(H2), p > 0. On the other hand, we revisit the classical case of composition operators on H2, giving first a new, and simplier, characterization of closed range composition operators, and then showing directly the equivalence of the two characterizations of membership in the Schatten classes of Luecking and Luecking and Zhu.
publishDate 2012
dc.date.none.fl_str_mv 2012
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/46376
https://doi.org/10.4171/RMI/666
url http://hdl.handle.net/11441/46376
https://doi.org/10.4171/RMI/666
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Revista Matemática Iberoamericana, 28 (1), 57-76.
MTM2006-05622
http://www.ems-ph.org/journals/show_pdf.php?issn=0213-2230&vol=28&iss=1&rank=3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society
publisher.none.fl_str_mv European Mathematical Society
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,198674

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