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

[摘要] 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.

[学科分类] 数学（综合）

[关键词] ð¶-𝑍 operator;characteristic atoms;$W L^1$;Hardy–Littlewood maximal operator;*-maximal operator.