Artículo
Interpolation of Vector Measures
Autor/es | Campo Acosta, Ricardo del
![]() ![]() ![]() ![]() ![]() ![]() Fernández Carrión, Antonio ![]() ![]() ![]() ![]() ![]() ![]() ![]() Mayoral Masa, Fernando ![]() ![]() ![]() ![]() ![]() ![]() ![]() Naranjo Naranjo, Francisco José Sánchez Pérez, Enrique A. |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Fecha de publicación | 2011 |
Fecha de depósito | 2022-07-26 |
Publicado en |
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Resumen | 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 ... 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. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España |
Identificador del proyecto | MTM2006–11690–C02
![]() MTM2009-14483-C02 ![]() |
Cita | Campo Acosta, R.d., Fernández Carrión, A., Mayoral Masa, F., Naranjo Naranjo, F.J. y Sánchez Pérez, E.A. (2011). Interpolation of Vector Measures. Acta Mathematica Sinica, English Series, 27 (1), 119-134. |
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