Tent spaces over metric measure spaces under doubling and related assumptions

TL;DR

This paper introduces and analyzes Coifman-Meyer-Stein tent spaces on metric measure spaces with minimal assumptions, establishing fundamental properties like duality, interpolation, and change of aperture.

Contribution

It defines tent spaces in general metric measure spaces and proves key functional analysis properties under minimal geometric conditions.

Findings

Established duality, interpolation, and change of aperture theorems for tent spaces.

Provided detailed proofs suitable for abstract metric measure spaces.

Extended the theory of tent spaces beyond classical Euclidean settings.

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.