Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces

We prove in this paper the existence of dense linear subspaces in the classical holomorphic Lipschitz spaces in the disc all of whose non-null functions are nowhere differentiable at the boundary. Infinitely generated free algebras as well as infinite dimensional Banach spaces consisting of Lipschit...

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Detalles Bibliográficos
Autores: Bernal González, Luis, Bonilla Ramírez, Antonio Lorenzo, López-Salazar Codes, Jerónimo, Seoane Sepúlveda, Juan Benigno
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2018
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/87514
Acceso en línea:https://hdl.handle.net/11441/87514
https://doi.org/10.1007/s00009-018-1160-6
Access Level:acceso abierto
Palabra clave:Disc algebra
Nowhere differentiable function
α-lipschitzian function
Lineability
Spaceability
Algebrability
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spelling Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spacesBernal González, LuisBonilla Ramírez, Antonio LorenzoLópez-Salazar Codes, JerónimoSeoane Sepúlveda, Juan BenignoDisc algebraNowhere differentiable functionα-lipschitzian functionLineabilitySpaceabilityAlgebrabilityWe prove in this paper the existence of dense linear subspaces in the classical holomorphic Lipschitz spaces in the disc all of whose non-null functions are nowhere differentiable at the boundary. Infinitely generated free algebras as well as infinite dimensional Banach spaces consisting of Lipschitz functions enjoying the mentioned property almost everywhere on the boundary are also exhibited. It is also investigated the algebraic size of the family of functions in the disc algebra that either do not preserve Borel sets on the unit circle or possess the Cantor boundary behavior on the disc.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y Competitividad (MINECO). EspañaSpringerAnálisis MatemáticoFQM127: Análisis Funcional no Lineal2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/87514https://doi.org/10.1007/s00009-018-1160-6reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMediterranean Journal of Mathematics, 15 (114), 1-20.FQM-127P08-FQM-03543MTM2015-65242-C2-1-PMTM2016-75963-PMTM2015-65825-Phttps://link.springer.com/content/pdf/10.1007%2Fs00009-018-1160-6.pdfinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/875142026-06-17T12:51:07Z
dc.title.none.fl_str_mv Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces
title Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces
spellingShingle Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces
Bernal González, Luis
Disc algebra
Nowhere differentiable function
α-lipschitzian function
Lineability
Spaceability
Algebrability
title_short Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces
title_full Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces
title_fullStr Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces
title_full_unstemmed Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces
title_sort Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces
dc.creator.none.fl_str_mv Bernal González, Luis
Bonilla Ramírez, Antonio Lorenzo
López-Salazar Codes, Jerónimo
Seoane Sepúlveda, Juan Benigno
author Bernal González, Luis
author_facet Bernal González, Luis
Bonilla Ramírez, Antonio Lorenzo
López-Salazar Codes, Jerónimo
Seoane Sepúlveda, Juan Benigno
author_role author
author2 Bonilla Ramírez, Antonio Lorenzo
López-Salazar Codes, Jerónimo
Seoane Sepúlveda, Juan Benigno
author2_role author
author
author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM127: Análisis Funcional no Lineal
dc.subject.none.fl_str_mv Disc algebra
Nowhere differentiable function
α-lipschitzian function
Lineability
Spaceability
Algebrability
topic Disc algebra
Nowhere differentiable function
α-lipschitzian function
Lineability
Spaceability
Algebrability
description We prove in this paper the existence of dense linear subspaces in the classical holomorphic Lipschitz spaces in the disc all of whose non-null functions are nowhere differentiable at the boundary. Infinitely generated free algebras as well as infinite dimensional Banach spaces consisting of Lipschitz functions enjoying the mentioned property almost everywhere on the boundary are also exhibited. It is also investigated the algebraic size of the family of functions in the disc algebra that either do not preserve Borel sets on the unit circle or possess the Cantor boundary behavior on the disc.
publishDate 2018
dc.date.none.fl_str_mv 2018
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 https://hdl.handle.net/11441/87514
https://doi.org/10.1007/s00009-018-1160-6
url https://hdl.handle.net/11441/87514
https://doi.org/10.1007/s00009-018-1160-6
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mediterranean Journal of Mathematics, 15 (114), 1-20.
FQM-127
P08-FQM-03543
MTM2015-65242-C2-1-P
MTM2016-75963-P
MTM2015-65825-P
https://link.springer.com/content/pdf/10.1007%2Fs00009-018-1160-6.pdf
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 Springer
publisher.none.fl_str_mv Springer
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 15,300724

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