Inhomogeneous cancellation conditions and Calderón-Zygmund type operators on $h^p$

Abstract

In this work we present a new approach to molecules on Goldberg's local Hardy spaces $h^p({\mathbb{R}}^n)$, $0<p\le 1$, assuming an appropriate cancellation condition. As applications, we prove a version of Hardy's inequality and improved continuity results for inhomogeneous Calderón-Zygmund operators on these spaces.

18 pages