Orlicz spaces associated to a quasi-Banach function space. Applications to vector measures and interpolation
Functional Analysis
2019-10-30 v1
Abstract
We characterize the relatively compact subsets of the quasi-Banach function space associated to the semivariation of a given vector measure showing that the strong connection between compactness, uniform absolute continuity, uniform integrability, almost order boundedness and L-weak compactness that appears in the classic setting of Lebesgue spaces remains almost invariant in this new context of the Choquet integration. Also we present a de la Vall\'ee-Poussin type theorem in the context of these spaces that allows us to locate each compact subset of as a compact subset of a smaller quasi-Banach Orlicz space associated to the semivariation of the measure
Keywords
Cite
@article{arxiv.1910.13183,
title = {Orlicz spaces associated to a quasi-Banach function space. Applications to vector measures and interpolation},
author = {Ricardo del Campo and Antonio Fernández and Fernando Mayoral and Francisco Naranjo},
journal= {arXiv preprint arXiv:1910.13183},
year = {2019}
}