The Hilbert transform of a measure

被引：0

作者：

Alexei Poltoratski

Barry Simon

Maxim Zinchenko

机构：

[1] Texas A&M University,Mathematics Department

[2] California Institute of Technology,Mathematics 253

来源：

Journal d'Analyse Mathématique | 2010年 / 111卷

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D O I：

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中图分类号：

学科分类号：

摘要：

Let e be a homogeneous subset of ℝ in the sense of Carleson. Let µ be a finite positive measure on ℝ and Hµ(x) its Hilbert transform. We prove that if limt→∞t|e∩{x ‖Hµ(x)| > t}| = 0, then µs(e) = 0, where µs is the singular part of µ.

引用

页码：247 / 265

页数：18

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