L¹-spaces of vector measures with vector density

2019/02/13 by Celia Avalos-Ramos, Avalos-Ramos, Celia
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1902.05154

Abstract

Let F be a function with values in a Banach space. When F is locally (Pettis or Bochner) integrable with respect to a locally determined positive measure, a vector measure ν_F with density F defined on a δ-ring is obtained. We present the existing connection between the spaces L¹_w(ν_F), L¹(ν_F) and L¹(|ν_F|) and the spaces of Dunford, Pettis or Bochner integrable functions.

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