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

共 17 条

[1] [Anonymous], 2002, Trigonometric Series
[2] [Anonymous], REFLECTIONLESS MEASU
[3] [Anonymous], 1857, Philosophical Transactions of the Royal Society of London
[4] CARLESON L, 1983, P C HARM AN HON ANT, V1, P349
[5] WEAK TYPE (1,1) INEQUALITY FOR CONJUGATE FUNCTIONS
DAVIS, B
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 44 (02) : 307 - 311
[6] DISTRIBUTIONS OF CONJUGATE FUNCTIONS OF NONNEGATIVE MEASURES
DAVIS, B
[J]. DUKE MATHEMATICAL JOURNAL, 1973, 40 (03) : 695 - 700
[7] Operators with singular continuous spectrum .4. Hausdorff dimensions, rank one perturbations, and localization
delRio, R
Jitomirskaya, S
Last, Y
Simon, B
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 1996, 69 : 153 - 200
[8] Local spectral properties of reflectionless Jacobi, CMV, and Schrodinger operators
Gesztesy, Fritz
Zinchenko, Maxim
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (01) : 78 - 107
[9] Hruscev S.V., 1981, LECT NOTES MATH, V864, P171
[10] A NOTE ON THE HILBERT TRANSFORM
LOOMIS, LH
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1946, 52 (12) : 1082 - 1091

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