Estimates for the maximal Cauchy integral on chord-arc curves

Carmelo Puliatti

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    © 2018, Annales Academiæ Scientiarum Fennicæ Mathematica. We study the chord-arc Jordan curves that satisfy the Cotlar-type inequality T*(f) ≲ M2(T f), where T is the Cauchy transform, T* is the maximal Cauchy transform and M is the Hardy-Littlewood maximal function. Under the background assumption of asymptotic conformality we find a characterization of such curves in terms of the smoothness of a parametrization of the curve.
    Original languageEnglish
    Pages (from-to)961-980
    JournalAnnales Academiae Scientiarum Fennicae Mathematica
    Volume43
    DOIs
    Publication statusPublished - 1 Jan 2018

    Keywords

    • Asymptotically conformal curve
    • Cauchy integral
    • Chord-arc curve
    • Cotlar's inequality

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