Calder\'on-Zygmund operators on local hardy spaces

TL;DR

This paper establishes precise conditions under which inhomogeneous Calderón-Zygmund operators are bounded on local Hardy spaces, with applications to Riesz transforms and pseudo-differential operators.

Contribution

It provides necessary and sufficient criteria for boundedness of these operators on local Hardy spaces, extending previous understanding.

Findings

Characterization of boundedness conditions for Calderón-Zygmund operators

Applications to local and truncated Riesz transforms

Extensions to pseudo-differential operators with amplitudes

Abstract

We give necessary and sufficient conditions for inhomogeneous Calder\'on-Zgymund operators to be bounded on the local hardy spaces $h^p(\mathbb{R}^n)$. We then give applications to local and truncated Riesz transforms, as well as pseudo-differential operators defined by amplitudes.