Orlicz boundedness for certain classical operators

Autores
Harboure, Eleonor Ofelia; Salinas, Oscar Mario; Viviani, Beatriz Eleonora
Año de publicación
2002
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let ɸ and ψ be functions defined on [0,∞) taking the value zero at zero and with non-negative continuous derivative. Under very mild extra assumptions we find necessary and sufficient conditions for the fractional maximal operator M∞Ω, associated to an open bounded set Ω, to be bounded from the Orlicz space Lψ(Ω) into Lɸ(Ω), 0 ≤ α < n. For functions ɸ of finite upper type these results can be extended to the Hilbert transform f on the one-dimensional torus and to the fractional integral operator IαΩ, 0 < α < n. Since these operators are linear and self-adjoint we get, by duality, boundedness results near infinity, deriving in this way some generalized Trudinger type inequalities.
Fil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Salinas, Oscar Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Viviani, Beatriz Eleonora. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
BOUNDEDNESS
FRACTIONAL INTEGRAL
HILBERT TRANSFORM
MAXIMAL FUNCTION
ORLICZ 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:11336/100607
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/100607
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Orlicz boundedness for certain classical operatorsHarboure, Eleonor OfeliaSalinas, Oscar MarioViviani, Beatriz EleonoraBOUNDEDNESSFRACTIONAL INTEGRALHILBERT TRANSFORMMAXIMAL FUNCTIONORLICZ SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let ɸ and ψ be functions defined on [0,∞) taking the value zero at zero and with non-negative continuous derivative. Under very mild extra assumptions we find necessary and sufficient conditions for the fractional maximal operator M∞Ω, associated to an open bounded set Ω, to be bounded from the Orlicz space Lψ(Ω) into Lɸ(Ω), 0 ≤ α < n. For functions ɸ of finite upper type these results can be extended to the Hilbert transform f on the one-dimensional torus and to the fractional integral operator IαΩ, 0 < α < n. Since these operators are linear and self-adjoint we get, by duality, boundedness results near infinity, deriving in this way some generalized Trudinger type inequalities.Fil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Salinas, Oscar Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Viviani, Beatriz Eleonora. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaInstitute of Mathematics - Polish Academy of Sciencies2002-06info: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/11336/100607Harboure, Eleonor Ofelia; Salinas, Oscar Mario; Viviani, Beatriz Eleonora; Orlicz boundedness for certain classical operators; Institute of Mathematics - Polish Academy of Sciencies; Colloquium Mathematicum; 91; 2; 6-2002; 263-2820010-1354CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4064/cm91-2-6info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:56:26Zoai:ri.conicet.gov.ar:11336/100607instacron: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:34982025-09-03 09:56:27.078CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Orlicz boundedness for certain classical operators
title Orlicz boundedness for certain classical operators
spellingShingle Orlicz boundedness for certain classical operators
Harboure, Eleonor Ofelia
BOUNDEDNESS
FRACTIONAL INTEGRAL
HILBERT TRANSFORM
MAXIMAL FUNCTION
ORLICZ SPACES
title_short Orlicz boundedness for certain classical operators
title_full Orlicz boundedness for certain classical operators
title_fullStr Orlicz boundedness for certain classical operators
title_full_unstemmed Orlicz boundedness for certain classical operators
title_sort Orlicz boundedness for certain classical operators
dc.creator.none.fl_str_mv Harboure, Eleonor Ofelia
Salinas, Oscar Mario
Viviani, Beatriz Eleonora
author Harboure, Eleonor Ofelia
author_facet Harboure, Eleonor Ofelia
Salinas, Oscar Mario
Viviani, Beatriz Eleonora
author_role author
author2 Salinas, Oscar Mario
Viviani, Beatriz Eleonora
author2_role author
author
dc.subject.none.fl_str_mv BOUNDEDNESS
FRACTIONAL INTEGRAL
HILBERT TRANSFORM
MAXIMAL FUNCTION
ORLICZ SPACES
topic BOUNDEDNESS
FRACTIONAL INTEGRAL
HILBERT TRANSFORM
MAXIMAL FUNCTION
ORLICZ 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 Let ɸ and ψ be functions defined on [0,∞) taking the value zero at zero and with non-negative continuous derivative. Under very mild extra assumptions we find necessary and sufficient conditions for the fractional maximal operator M∞Ω, associated to an open bounded set Ω, to be bounded from the Orlicz space Lψ(Ω) into Lɸ(Ω), 0 ≤ α < n. For functions ɸ of finite upper type these results can be extended to the Hilbert transform f on the one-dimensional torus and to the fractional integral operator IαΩ, 0 < α < n. Since these operators are linear and self-adjoint we get, by duality, boundedness results near infinity, deriving in this way some generalized Trudinger type inequalities.
Fil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Salinas, Oscar Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Viviani, Beatriz Eleonora. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description Let ɸ and ψ be functions defined on [0,∞) taking the value zero at zero and with non-negative continuous derivative. Under very mild extra assumptions we find necessary and sufficient conditions for the fractional maximal operator M∞Ω, associated to an open bounded set Ω, to be bounded from the Orlicz space Lψ(Ω) into Lɸ(Ω), 0 ≤ α < n. For functions ɸ of finite upper type these results can be extended to the Hilbert transform f on the one-dimensional torus and to the fractional integral operator IαΩ, 0 < α < n. Since these operators are linear and self-adjoint we get, by duality, boundedness results near infinity, deriving in this way some generalized Trudinger type inequalities.
publishDate 2002
dc.date.none.fl_str_mv 2002-06
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/11336/100607
Harboure, Eleonor Ofelia; Salinas, Oscar Mario; Viviani, Beatriz Eleonora; Orlicz boundedness for certain classical operators; Institute of Mathematics - Polish Academy of Sciencies; Colloquium Mathematicum; 91; 2; 6-2002; 263-282
0010-1354
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100607
identifier_str_mv Harboure, Eleonor Ofelia; Salinas, Oscar Mario; Viviani, Beatriz Eleonora; Orlicz boundedness for certain classical operators; Institute of Mathematics - Polish Academy of Sciencies; Colloquium Mathematicum; 91; 2; 6-2002; 263-282
0010-1354
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4064/cm91-2-6
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 Institute of Mathematics - Polish Academy of Sciencies
publisher.none.fl_str_mv Institute of Mathematics - Polish Academy of Sciencies
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 13.13397

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