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
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad de Burgos (UBU)
Repositorio:Repositorio Institucional de la Universidad de Burgos (RIUBU)
OAI Identifier:oai:riubu.ubu.es:10259/9751
Acceso en línea:http://hdl.handle.net/10259/9751
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
Análisis matemático
Mathematical analysis
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.