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Lp-continuity for Calderón-Zygmund operator

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Abstract

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.

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Authors and Affiliations

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

    Q. X. Yang

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  1. Q. X. Yang
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Correspondence to Q. X. Yang.

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Yang, Q.X. Lp-continuity for Calderón-Zygmund operator. Proc. Indian Acad. Sci. (Math. Sci.) 115, 191–200 (2005). https://doi.org/10.1007/BF02829625

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  • DOI: https://doi.org/10.1007/BF02829625

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