Compact $T(1)$ theorem \`a la Stein

TL;DR

This paper establishes a compact version of the classical T(1) theorem with quantitative estimates, extending the understanding of Calderón-Zygmund operators' mapping properties.

Contribution

It introduces a compact T(1) theorem with quantitative bounds and explores the mapping properties of non-compact Calderón-Zygmund operators.

Findings

Proved a compact T(1) theorem with explicit estimates.

Analyzed the C_c^∞ to CMO mapping properties of non-compact Calderón-Zygmund operators.

Extended classical results to a compact setting with quantitative control.

Abstract

We prove a compact $T(1)$ theorem, involving quantitative estimates, analogous to the quantitative classical $T(1)$ theorem due to Stein. We also discuss the $C_c^\infty$-to-$CMO$ mapping properties of non-compact Calder\'on-Zygmund operators.