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

Q X Yang

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

Q X Yang

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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 $WL^{1}$, 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.

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BibTeX RIS

Q X Yang. 2006-07-26. $L^p$-continuity for Calderón--Zygmund operator. https://arxiv.org/abs/math/0607657

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