• $L^p$-Continuity for Calderón–Zygmund Operator

• Fulltext

http://www.ias.ac.in/article/fulltext/pmsc/115/02/0191-0200

• Keywords

𝐶-𝑍 operator; characteristic atoms; $W L^1$; Hardy–Littlewood maximal operator; *-maximal 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 $L^p(1 < p < ∞)$. So the study of strong continuity on arbitrary function in $L^p$ has been changed into the study of weak continuity on characteristic functions.

• Author Affiliations

1. Department of Mathematics, Wuhan University, 430072 Hubei, China

• Proceedings – Mathematical Sciences

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Volume 127 | Issue 5
November 2017