Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 961-980

ESTIMATES FOR THE MAXIMAL CAUCHY INTEGRAL ON CHORD-ARC CURVES

Carmelo Puliatti

Universitat Autònoma de Barcelona, BGSMath and Departament de Matemàtiques
08193, Bellaterra, Barcelona, Catalonia; puliatti 'at' mat.uab.cat

Abstract. We study the chord-arc Jordan curves that satisfy the Cotlar-type inequality T_*(f) ≤ M²(Tf), 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.

2010 Mathematics Subject Classification: Primary 42B20, 30C62, 28A80.

Key words: Cauchy integral, Cotlar's inequality, asymptotically conformal curve, chord-arc curve.

Reference to this article: C. Puliatti: Estimates for the maximal Cauchy integral on chord-arc curves. Ann. Acad. Sci. Fenn. Math. 43 (2018), 961-980.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4362