L p -continuity for Calderón-Zygmund operator



Given a Calderón-Zygmund (C-Z for short) operatorT, which satisfies Hörmander condition, we prove that: ifT maps all the characteristic atoms toWL 1, thenT is continuous fromL p toL p (1 <p < ∞). So the study of strong continuity on arbitrary function inL p has been changed into the study of weak continuity on characteristic functions.


C-Z operator characteristic atoms WL1 Hardy-Littlewood maximal operator *-maximal operator 


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© Indian Academy of Sciences 2005

Authors and Affiliations

  1. 1.Department of MathematicsWuhan UniversityHubeiChina

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