On spaces of integrable functions associated to vector measures and limiting real interpolation

We investigate which spaces are obtained when considering the limiting class of real interpolation spaces (0, q; J) for ordered Banach couples of spaces of (scalar) integrable functions with respect to a vector measure m, defined on a σ-algebra, with values in a Banach space. If m is in particular a...

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Detalles Bibliográficos
Autores: Fernández Carrión, Antonio, Manzano Rodríguez, Antonio, Journal of Mathematical Analysis and Applications (Coordinador)
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/164113
Acceso en línea:https://hdl.handle.net/11441/164113
https://doi.org/10.1016/j.jmaa.2024.128573
Access Level:acceso abierto
Palabra clave:Extreme interpolation spaces
Vector measures
Lorentz-Zygmund spaces
Optimal domain
p-th power factorable operators
Bidual (p, q)-power-concave operators
Descripción
Sumario:We investigate which spaces are obtained when considering the limiting class of real interpolation spaces (0, q; J) for ordered Banach couples of spaces of (scalar) integrable functions with respect to a vector measure m, defined on a σ-algebra, with values in a Banach space. If m is in particular a finite positive scalar measure, previous known results are derived from ours. Furthermore, we study the interpolation of p-th power factorable operators by the extreme real interpolation method (1, q; K). We also deduce interpolation results for the (1, q; K)-method that apply to other related classes of operators to p-th power factorable operators, such as bidual (p, q)-power-concave operators and q-concave operators.