Weighted Discrete Hardy Inequalities on Trees and Applications

Autores
López-García, Fernando; Ojea, Ignacio
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on Hölder-α domains, where the weights are powers of the distance to the boundary. We obtain results regarding the divergence equation’s solvability, and the improved Poincaré, the fractional Poincaré, and the Korn inequalities. The proofs are based on a local-to-global argument that involves a kind of atomic decomposition of functions and the validity of a weighted discrete Hardy-type inequality on trees. The novelty of our approach lies in the use of this weighted discrete Hardy inequality and a sufficient condition that allows us to study the weights of our interest. As a consequence, the assumptions on the weight exponents that appear in our results are weaker than those in the literature.
Fil: López-García, Fernando. California State Polytechnic University; Estados Unidos
Fil: Ojea, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
DECOMPOSITION OF FUNCTIONS
DISCRETE HARDY INEQUALITY
DISTANCE
DIVERGENCE EQUATION
HÖLDER-Α DOMAINS
KORN’S INEQUALITY
POINCARÉ-TYPE INEQUALITIES
TREES
WEIGHTS
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:11336/213628
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/213628
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Weighted Discrete Hardy Inequalities on Trees and ApplicationsLópez-García, FernandoOjea, IgnacioDECOMPOSITION OF FUNCTIONSDISCRETE HARDY INEQUALITYDISTANCEDIVERGENCE EQUATIONHÖLDER-Α DOMAINSKORN’S INEQUALITYPOINCARÉ-TYPE INEQUALITIESTREESWEIGHTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on Hölder-α domains, where the weights are powers of the distance to the boundary. We obtain results regarding the divergence equation’s solvability, and the improved Poincaré, the fractional Poincaré, and the Korn inequalities. The proofs are based on a local-to-global argument that involves a kind of atomic decomposition of functions and the validity of a weighted discrete Hardy-type inequality on trees. The novelty of our approach lies in the use of this weighted discrete Hardy inequality and a sufficient condition that allows us to study the weights of our interest. As a consequence, the assumptions on the weight exponents that appear in our results are weaker than those in the literature.Fil: López-García, Fernando. California State Polytechnic University; Estados UnidosFil: Ojea, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaSpringer2022-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/213628López-García, Fernando; Ojea, Ignacio; Weighted Discrete Hardy Inequalities on Trees and Applications; Springer; Potential Analysis; 59; 2; 1-2022; 675-7030926-2601CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11118-021-09982-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:08:25Zoai:ri.conicet.gov.ar:11336/213628instacron: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:34982025-09-29 10:08:26.217CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Weighted Discrete Hardy Inequalities on Trees and Applications
title Weighted Discrete Hardy Inequalities on Trees and Applications
spellingShingle Weighted Discrete Hardy Inequalities on Trees and Applications
López-García, Fernando
DECOMPOSITION OF FUNCTIONS
DISCRETE HARDY INEQUALITY
DISTANCE
DIVERGENCE EQUATION
HÖLDER-Α DOMAINS
KORN’S INEQUALITY
POINCARÉ-TYPE INEQUALITIES
TREES
WEIGHTS
title_short Weighted Discrete Hardy Inequalities on Trees and Applications
title_full Weighted Discrete Hardy Inequalities on Trees and Applications
title_fullStr Weighted Discrete Hardy Inequalities on Trees and Applications
title_full_unstemmed Weighted Discrete Hardy Inequalities on Trees and Applications
title_sort Weighted Discrete Hardy Inequalities on Trees and Applications
dc.creator.none.fl_str_mv López-García, Fernando
Ojea, Ignacio
author López-García, Fernando
author_facet López-García, Fernando
Ojea, Ignacio
author_role author
author2 Ojea, Ignacio
author2_role author
dc.subject.none.fl_str_mv DECOMPOSITION OF FUNCTIONS
DISCRETE HARDY INEQUALITY
DISTANCE
DIVERGENCE EQUATION
HÖLDER-Α DOMAINS
KORN’S INEQUALITY
POINCARÉ-TYPE INEQUALITIES
TREES
WEIGHTS
topic DECOMPOSITION OF FUNCTIONS
DISCRETE HARDY INEQUALITY
DISTANCE
DIVERGENCE EQUATION
HÖLDER-Α DOMAINS
KORN’S INEQUALITY
POINCARÉ-TYPE INEQUALITIES
TREES
WEIGHTS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on Hölder-α domains, where the weights are powers of the distance to the boundary. We obtain results regarding the divergence equation’s solvability, and the improved Poincaré, the fractional Poincaré, and the Korn inequalities. The proofs are based on a local-to-global argument that involves a kind of atomic decomposition of functions and the validity of a weighted discrete Hardy-type inequality on trees. The novelty of our approach lies in the use of this weighted discrete Hardy inequality and a sufficient condition that allows us to study the weights of our interest. As a consequence, the assumptions on the weight exponents that appear in our results are weaker than those in the literature.
Fil: López-García, Fernando. California State Polytechnic University; Estados Unidos
Fil: Ojea, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on Hölder-α domains, where the weights are powers of the distance to the boundary. We obtain results regarding the divergence equation’s solvability, and the improved Poincaré, the fractional Poincaré, and the Korn inequalities. The proofs are based on a local-to-global argument that involves a kind of atomic decomposition of functions and the validity of a weighted discrete Hardy-type inequality on trees. The novelty of our approach lies in the use of this weighted discrete Hardy inequality and a sufficient condition that allows us to study the weights of our interest. As a consequence, the assumptions on the weight exponents that appear in our results are weaker than those in the literature.
publishDate 2022
dc.date.none.fl_str_mv 2022-01
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/11336/213628
López-García, Fernando; Ojea, Ignacio; Weighted Discrete Hardy Inequalities on Trees and Applications; Springer; Potential Analysis; 59; 2; 1-2022; 675-703
0926-2601
CONICET Digital
CONICET
url http://hdl.handle.net/11336/213628
identifier_str_mv López-García, Fernando; Ojea, Ignacio; Weighted Discrete Hardy Inequalities on Trees and Applications; Springer; Potential Analysis; 59; 2; 1-2022; 675-703
0926-2601
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s11118-021-09982-5
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
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.070432

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