Pointwise convergence to initial data of heat and Laplace equations

Autores
Garrigos Aniorte, Gustavo; Hartzstein, Silvia Inés; Signes, Teresa; Torrea Hernández, José Luis; Viviani, Beatriz Eleonora
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let L be either the Hermite or the Ornstein-Uhlenbeck operator on Rd. We find optimal integrability conditions on a function f for the existence of its heat and Poisson integrals, e−tLf(x) and e−t √Lf(x), solutions respectively of Ut = −LU and Utt = LU on Rd+1 + with initial datum f. As a consequence we identify the most general class of weights v(x) for which such solutions converge a.e. to f for all f ∈ Lp(v), and each p ∈ [1,∞). Moreover, if 1 Fil: Garrigos Aniorte, Gustavo. Universidad de Murcia; España
Fil: Hartzstein, Silvia Inés. 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: Signes, Teresa. Universidad de Murcia; España
Fil: Torrea Hernández, José Luis. Universidad Autónoma de Madrid; España
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
Hermite Operator
Ornstein-Uhlenbeck
Poisson integral
Weighted Inequalities
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/31895
Acceder
id CONICETDig_e9f416a9157e1672f886fa3132b7bed7
oai_identifier_str oai:ri.conicet.gov.ar:11336/31895
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Pointwise convergence to initial data of heat and Laplace equationsGarrigos Aniorte, GustavoHartzstein, Silvia InésSignes, TeresaTorrea Hernández, José LuisViviani, Beatriz EleonoraHermite OperatorOrnstein-UhlenbeckPoisson integralWeighted Inequalitieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let L be either the Hermite or the Ornstein-Uhlenbeck operator on Rd. We find optimal integrability conditions on a function f for the existence of its heat and Poisson integrals, e−tLf(x) and e−t √Lf(x), solutions respectively of Ut = −LU and Utt = LU on Rd+1 + with initial datum f. As a consequence we identify the most general class of weights v(x) for which such solutions converge a.e. to f for all f ∈ Lp(v), and each p ∈ [1,∞). Moreover, if 1 <p< ∞ we additionally show that for such weights the associated local maximal operators are strongly bounded from Lp(v) → Lp(u) for some other weight u(x).Fil: Garrigos Aniorte, Gustavo. Universidad de Murcia; EspañaFil: Hartzstein, Silvia Inés. 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: Signes, Teresa. Universidad de Murcia; EspañaFil: Torrea Hernández, José Luis. Universidad Autónoma de Madrid; EspañaFil: 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; ArgentinaAmerican Mathematical Society2016-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/31895Viviani, Beatriz Eleonora; Torrea Hernández, José Luis; Signes, Teresa; Hartzstein, Silvia Inés; Garrigos Aniorte, Gustavo; Pointwise convergence to initial data of heat and Laplace equations; American Mathematical Society; Transactions Of The American Mathematical Society; 368; 9-2016; 6575-66000002-9947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/tran/2016-368-09/S0002-9947-2016-06554-X/info:eu-repo/semantics/altIdentifier/doi/10.1090/tran/6554info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:43:43Zoai:ri.conicet.gov.ar:11336/31895instacron: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:34982025-10-15 15:43:43.999CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Pointwise convergence to initial data of heat and Laplace equations
title Pointwise convergence to initial data of heat and Laplace equations
spellingShingle Pointwise convergence to initial data of heat and Laplace equations
Garrigos Aniorte, Gustavo
Hermite Operator
Ornstein-Uhlenbeck
Poisson integral
Weighted Inequalities
title_short Pointwise convergence to initial data of heat and Laplace equations
title_full Pointwise convergence to initial data of heat and Laplace equations
title_fullStr Pointwise convergence to initial data of heat and Laplace equations
title_full_unstemmed Pointwise convergence to initial data of heat and Laplace equations
title_sort Pointwise convergence to initial data of heat and Laplace equations
dc.creator.none.fl_str_mv Garrigos Aniorte, Gustavo
Hartzstein, Silvia Inés
Signes, Teresa
Torrea Hernández, José Luis
Viviani, Beatriz Eleonora
author Garrigos Aniorte, Gustavo
author_facet Garrigos Aniorte, Gustavo
Hartzstein, Silvia Inés
Signes, Teresa
Torrea Hernández, José Luis
Viviani, Beatriz Eleonora
author_role author
author2 Hartzstein, Silvia Inés
Signes, Teresa
Torrea Hernández, José Luis
Viviani, Beatriz Eleonora
author2_role author
author
author
author
dc.subject.none.fl_str_mv Hermite Operator
Ornstein-Uhlenbeck
Poisson integral
Weighted Inequalities
topic Hermite Operator
Ornstein-Uhlenbeck
Poisson integral
Weighted Inequalities
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 L be either the Hermite or the Ornstein-Uhlenbeck operator on Rd. We find optimal integrability conditions on a function f for the existence of its heat and Poisson integrals, e−tLf(x) and e−t √Lf(x), solutions respectively of Ut = −LU and Utt = LU on Rd+1 + with initial datum f. As a consequence we identify the most general class of weights v(x) for which such solutions converge a.e. to f for all f ∈ Lp(v), and each p ∈ [1,∞). Moreover, if 1 <p< ∞ we additionally show that for such weights the associated local maximal operators are strongly bounded from Lp(v) → Lp(u) for some other weight u(x).
Fil: Garrigos Aniorte, Gustavo. Universidad de Murcia; España
Fil: Hartzstein, Silvia Inés. 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: Signes, Teresa. Universidad de Murcia; España
Fil: Torrea Hernández, José Luis. Universidad Autónoma de Madrid; España
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 L be either the Hermite or the Ornstein-Uhlenbeck operator on Rd. We find optimal integrability conditions on a function f for the existence of its heat and Poisson integrals, e−tLf(x) and e−t √Lf(x), solutions respectively of Ut = −LU and Utt = LU on Rd+1 + with initial datum f. As a consequence we identify the most general class of weights v(x) for which such solutions converge a.e. to f for all f ∈ Lp(v), and each p ∈ [1,∞). Moreover, if 1 <p< ∞ we additionally show that for such weights the associated local maximal operators are strongly bounded from Lp(v) → Lp(u) for some other weight u(x).
publishDate 2016
dc.date.none.fl_str_mv 2016-09
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/11336/31895
Viviani, Beatriz Eleonora; Torrea Hernández, José Luis; Signes, Teresa; Hartzstein, Silvia Inés; Garrigos Aniorte, Gustavo; Pointwise convergence to initial data of heat and Laplace equations; American Mathematical Society; Transactions Of The American Mathematical Society; 368; 9-2016; 6575-6600
0002-9947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/31895
identifier_str_mv Viviani, Beatriz Eleonora; Torrea Hernández, José Luis; Signes, Teresa; Hartzstein, Silvia Inés; Garrigos Aniorte, Gustavo; Pointwise convergence to initial data of heat and Laplace equations; American Mathematical Society; Transactions Of The American Mathematical Society; 368; 9-2016; 6575-6600
0002-9947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/tran/2016-368-09/S0002-9947-2016-06554-X/
info:eu-repo/semantics/altIdentifier/doi/10.1090/tran/6554
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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
_version_ 1846083541944762368
score 13.22299

Publicaciones similares