Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps

[EN] Given a countable set of families {Dk:k¿N} of pseudometrics over the same set D, we study the power-aggregations of this class, that are defined as convex combinations of integral averages of powers of the elements of ¿kDk. We prove that a Lipschitz function f is dominated by such a power-aggre...

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Detalles Bibliográficos
Autores: Rodríguez López, Jesús|||0000-0001-5141-9977, Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/166134
Acceso en línea:https://riunet.upv.es/handle/10251/166134
Access Level:acceso abierto
Palabra clave:Pseudometric
Aggregation
Lipschitz function
Extension
P-average
MATEMATICA APLICADA
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spelling Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace mapsRodríguez López, Jesús|||0000-0001-5141-9977Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154PseudometricAggregationLipschitz functionExtensionP-averageMATEMATICA APLICADA[EN] Given a countable set of families {Dk:k¿N} of pseudometrics over the same set D, we study the power-aggregations of this class, that are defined as convex combinations of integral averages of powers of the elements of ¿kDk. We prove that a Lipschitz function f is dominated by such a power-aggregation if and only if a certain property of super-additivity involving the powers of the elements of ¿kDk is fulfilled by f. In particular, we show that a pseudo-metric is equivalent to a power-aggregation of other pseudometrics if this kind of domination holds. When the super-additivity property involves a p-power domination, we say that the elements of Dk are p-concave. As an application of our results, we prove under this requirement a new extension result of McShane-Whitney type for Lipschitz p-concave real valued maps.Both authors gratefully acknowledge the support of the Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigaciones and FEDER under each grants MTM2015-64373-P (MINECO/FEDER, UE) and MTM2016-77054-C2-1-P.Springer-VerlagDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería de Caminos, Canales y PuertosAgencia Estatal de InvestigaciónEuropean Regional Development FundMinisterio de Economía y CompetitividadMinisterio de Ciencia, Innovación y UniversidadesRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-12-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/166134reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2016-77054-C2-1-P ANALISIS NO LINEAL, INTEGRACION VECTORIAL Y APLICACIONES EN CIENCIAS DE LA INFORMACIONMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2015-64373-P HIPERESPACIOS, ESTRUCTURAS DIFUSAS Y ASIMETRICAS. APLICACIONES A CIENCIA DE LA COMPUTACION Y AL FILTRADO DE IMAGENES.open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1661342026-06-13T07:49:27Z
dc.title.none.fl_str_mv Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps
title Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps
spellingShingle Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps
Rodríguez López, Jesús|||0000-0001-5141-9977
Pseudometric
Aggregation
Lipschitz function
Extension
P-average
MATEMATICA APLICADA
title_short Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps
title_full Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps
title_fullStr Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps
title_full_unstemmed Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps
title_sort Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps
dc.creator.none.fl_str_mv Rodríguez López, Jesús|||0000-0001-5141-9977
Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
author Rodríguez López, Jesús|||0000-0001-5141-9977
author_facet Rodríguez López, Jesús|||0000-0001-5141-9977
Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
author_role author
author2 Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos
Agencia Estatal de Investigación
European Regional Development Fund
Ministerio de Economía y Competitividad
Ministerio de Ciencia, Innovación y Universidades
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Pseudometric
Aggregation
Lipschitz function
Extension
P-average
MATEMATICA APLICADA
topic Pseudometric
Aggregation
Lipschitz function
Extension
P-average
MATEMATICA APLICADA
description [EN] Given a countable set of families {Dk:k¿N} of pseudometrics over the same set D, we study the power-aggregations of this class, that are defined as convex combinations of integral averages of powers of the elements of ¿kDk. We prove that a Lipschitz function f is dominated by such a power-aggregation if and only if a certain property of super-additivity involving the powers of the elements of ¿kDk is fulfilled by f. In particular, we show that a pseudo-metric is equivalent to a power-aggregation of other pseudometrics if this kind of domination holds. When the super-additivity property involves a p-power domination, we say that the elements of Dk are p-concave. As an application of our results, we prove under this requirement a new extension result of McShane-Whitney type for Lipschitz p-concave real valued maps.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-12-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/166134
url https://riunet.upv.es/handle/10251/166134
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2016-77054-C2-1-P ANALISIS NO LINEAL, INTEGRACION VECTORIAL Y APLICACIONES EN CIENCIAS DE LA INFORMACION
Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2015-64373-P HIPERESPACIOS, ESTRUCTURAS DIFUSAS Y ASIMETRICAS. APLICACIONES A CIENCIA DE LA COMPUTACION Y AL FILTRADO DE IMAGENES.
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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