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

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

2006-07-26

arxiv.org/abs/math/0607657v1

Mathematics

Classical Analysis and ODEs

9 pages

Scientific paper

Given a Calder\'{o}n--Zygmund (C--Z for short) operator $T$, which satisfies
H\"ormander condition, we prove that: if $T$ maps all the characteristic atoms
to $WL^{1}$, then $T$ is continuous from $L^{p}$ to $L^{p}(1study 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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