Tent spaces over metric measure spaces under doubling and related assumptions

Abstract

In this article, we define the Coifman-Meyer-Stein tent spaces $T^{p,q,\alpha}(X)$ associated with an arbitrary metric measure space $(X,d,\mu)$ under minimal geometric assumptions. While gradually strengthening our geometric assumptions, we prove duality, interpolation, and change of aperture theorems for the tent spaces. Because of the inherent technicalities in dealing with abstract metric measure spaces, most proofs are presented in full detail.