Spaces of Goldberg type on certain measured metric spaces

2016/04/07 by Stefano Meda, Sara Volpi, Meda, Stefano +1 · 1 citation
Mathematics · #43A17 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:43A17

paper · pdf · doi:10.48550/arxiv.1604.05154

arxiv created 2016/04/07 · arxiv updated 2016/04/19

Abstract

In this paper we define a space \ghuM of Hardy--Goldberg type on a measured metric space satisfying some mild conditions. We prove that the dual of \ghuM may be identified with \gbmoM, a space of functions with "local" bounded mean oscillation, and that if p is in (1,2), then \lpM is a complex interpolation space between \ghuM and \ldM. This extends previous results of Strichartz, Carbonaro, Mauceri and Meda, and Taylor. Applications to singular integral operators on Riemannian manifolds are given.

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