$L^p$-continuity for Calderón--Zygmund operator

Abstract

Given a Calderón--Zygmund (C--Z for short) operator $T$, which satisfies Hörmander condition, we prove that: if $T$ maps all the characteristic atoms to $W{L}^1$, then $T$ is continuous from $L^p$ to $L^p(1<p<\infty )$. So the study of strong continuity on arbitrary function in $L^p$ has been changed into the study of weak continuity on characteristic functions.

9 pages