COUNTEREXAMPLES TO SOME POINTWISE ESTIMATES OF THE MAXIMAL CAUCHY TRANSFORM IN TERMS OF THE CAUCHY TRANSFORM

被引：2

作者：

Girela-Sarrion, Daniel ^{[1
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Barcelona, Spain

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2013年 / 38卷 / 02期

基金：

欧洲研究理事会;

关键词：

Calderon-Zygmund theory; Cauchy transform; Cotlar's inequality;

D O I：

10.5186/aasfm.2013.3828

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Motivated by the work of Mateu, Orobitg, Perez and Verdera, who proved inequalities of the form T(*)f less than or similar to M(Tf) or T(*)f less than or similar to M-2 (Tf) for certain singular integral operators T, such as the Hilbert or the Beurling transforms, we study the possibility of establishing this type of control when T is the Cauchy transform along a Lipschitz graph. We show that this is not possible in general, and we give a partial positive result when the graph is substituted by a Jordan curve.

引用

页码：657 / 675

页数：19

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