Weighted tent spaces with Whitney averages: factorization, interpolation and duality

TL;DR

This paper introduces a new class of weighted tent spaces that unify and extend existing spaces, providing new factorization, interpolation, and duality results with applications to elliptic equations.

Contribution

It develops a new scale of tent spaces covering several known types, establishing strong factorizations, interpolation, and duality results, unifying previous theories.

Findings

Established strong factorizations within the new tent spaces.

Applied results to quasi-Banach complex interpolation.

Extended duality theory for weighted tent spaces.

Abstract

In this paper, we introduce a new scale of tent spaces which covers, the (weighted) tent spaces of Coifman-Meyer-Stein and of Hofmann-Mayboroda-McIntosh, and some other tent spaces considered by Dahlberg, Kenig-Pipher and Auscher-Axelsson in elliptic equations. The strong factorizations within our tent spaces, with applications to quasi-Banach complex interpolation and to multiplier-duality theory, are established. This way, we unify and extend the corresponding results obtained by Coifman-Meyer-Stein, Cohn-Verbitsky and Hyt\"onen-Ros\'en.