Interpolation of Vector Measures
Let (Ω, Σ) be a measurable space and m 0: Σ → X 0 and m 1: Σ → X 1 be positive vector measures with values in the Banach Köthe function spaces X 0 and X 1. If 0 < α < 1, we define a new vector measure [m 0, m 1] α with values in the Calderón lattice interpolation space X 1−ga0 X α1 and we anal...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/135784 |
| Acceso en línea: | https://hdl.handle.net/11441/135784 https://doi.org/10.1007/s10114-011-9542-8 |
| Access Level: | acceso abierto |
| Palabra clave: | Interpolation Banach function space Vector measures |
| Sumario: | Let (Ω, Σ) be a measurable space and m 0: Σ → X 0 and m 1: Σ → X 1 be positive vector measures with values in the Banach Köthe function spaces X 0 and X 1. If 0 < α < 1, we define a new vector measure [m 0, m 1] α with values in the Calderón lattice interpolation space X 1−ga0 X α1 and we analyze the space of integrable functions with respect to measure [m 0, m 1] α in order to prove suitable extensions of the classical Stein-Weiss formulas that hold for the complex interpolation of L p-spaces. Since each p-convex order continuous Köthe function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces. |
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