Spaces of Goldberg type on certain measured metric spaces

Abstract

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