Uniform sparse bounds for discrete quadratic phase Hilbert transforms

被引：4

作者：

Kesler, Robert ^{[1
]}

Arias, Dario Mena ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, 686 Cherry St, Atlanta, GA 30312 USA

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2019年 / 9卷 / 01期

关键词：

Discrete analysis; Quadratic phase; Sparse bounds;

D O I：

10.1007/s13324-017-0195-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For each a. T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z. C according to Ha f ( n) :=m = 0 eiam2 f ( n - m) m. We prove that, uniformly in a. T, there is a sparse bound for the bilinear formHa f, g for every pair of finitely supported functions f, g : Z. C. The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Holder classes.

引用

页码：263 / 274

页数：12

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