EXTENSION OF LIPSCHITZ-TYPE OPERATORS ON BANACH FUNCTION SPACES

[EN] We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and other measure-theoretic notions are introduced. We analyze...

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Detalles Bibliográficos
Autores: Cavalcante, Wasthenny, V., Rueda, Pilar, Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
Tipo de recurso: artículo
Fecha de publicación:2021
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:10251/186798
Acceso en línea:https://riunet.upv.es/handle/10251/186798
Access Level:acceso abierto
Palabra clave:Lipschitz operator
Banach function space
Integration
Measure
Metric space
MATEMATICA APLICADA
Descripción
Sumario:[EN] We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and other measure-theoretic notions are introduced. We analyze Lipschitz-type inequalities in two fundamental cases. The first concerns almost everywhere pointwise inequalities, while the second considers dominations involving integrals. These Lipschitz-type inequalities provide a suitable frame to work with operators that take values on Banach function spaces. In the last part of the paper we use some interpolation procedures to extend our study to interpolated Banach function spaces.