A characterization of compactness for singular integrals

TL;DR

This paper establishes a comprehensive T(1) Theorem that characterizes when Calderon-Zygmund singular integral operators are compact on L^p spaces, providing both necessary and sufficient conditions.

Contribution

It introduces a complete characterization of compactness for Calderon-Zygmund operators via a T(1) Theorem, advancing understanding of singular integral operator behavior.

Findings

Provides necessary and sufficient conditions for compactness

Characterizes compactness of singular integrals on L^p(R)

Advances theoretical understanding of Calderon-Zygmund operators

Abstract

We prove a T(1) Theorem to completely characterize compactness of Calderon-Zygmund operators. The result provides sufficient and necessary conditions for the compactness of singular integral operators acting on L^p(R).