TY - JOUR
T1 - Estimates for the maximal Cauchy integral on chord-arc curves
AU - Puliatti, Carmelo
PY - 2018/1/1
Y1 - 2018/1/1
N2 - © 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.
AB - © 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.
KW - Asymptotically conformal curve
KW - Cauchy integral
KW - Chord-arc curve
KW - Cotlar's inequality
UR - https://www.scopus.com/pages/publications/85055627318
U2 - 10.5186/AASFM.2018.4362
DO - 10.5186/AASFM.2018.4362
M3 - Article
SN - 1239-629X
VL - 43
SP - 961
EP - 980
JO - Annales Academiae Scientiarum Fennicae Mathematica
JF - Annales Academiae Scientiarum Fennicae Mathematica
ER -