THE HILBERT TRANSFORM OF A MEASURE

被引：15

作者：

Poltoratski, Alexei ^{[1
]}

Simon, Barry ^{[2
]}

Zinchenko, Maxim ^{[2
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] CALTECH, Pasadena, CA 91125 USA

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2010年 / 111卷

基金：

美国国家科学基金会;

关键词：

CONJUGATE FUNCTIONS; DISTRIBUTIONS; OPERATORS;

D O I：

10.1007/s11854-010-0017-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let e be a homogeneous subset of R in the sense of Carleson. Let mu be a finite positive measure on R and H(mu)(x) its Hilbert transform. We prove that if lim(t ->infinity) t|e boolean AND{x vertical bar vertical bar H(mu)(x)| > t}| = 0, then mu(s)(e) = 0, where mu(s) is the singular part of mu.

引用

页码：247 / 265

页数：19

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