Geometric conditions for the L 2 -boundedness of singular integral operators with odd kernels with respect to measures with polynomial growth in ℝ d

Daniel Girela-Sarrión

    Research output: Contribution to journalArticleResearch

    1 Citation (Scopus)

    Abstract

    © 2019, The Hebrew University of Jerusalem. Let μ be a finite Radon measure in ℝ d with polynomial growth of degree n, although not necessarily n-AD regular. We prove that under some geometric conditions on μ that are closely related to rectifiability and involve the so-called β-numbers of Jones, David and Semmes, all singular integral operators with an odd and sufficiently smooth Calderón-Zygmund kernel are bounded in L 2 (μ). As a corollary, we obtain a lower bound for the Lipschitz harmonic capacity of a compact set in ℝ d only in terms of its metric and geometric properties.
    Original languageEnglish
    Pages (from-to)339-372
    JournalJournal d'Analyse Mathematique
    Volume137
    DOIs
    Publication statusPublished - 1 Mar 2019

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