Campo Acosta, Ricardo delFernández Carrión, AntonioMayoral Masa, FernandoNaranjo Naranjo, Francisco JoséSánchez Pérez, Enrique A.2022-07-262022-07-262011Campo 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), 119-134.1439-8516https://hdl.handle.net/11441/135784Let (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.application/pdf16engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/InterpolationBanach function spaceVector measuresinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/s10114-011-9542-8