UNIFORM ESTIMATES FOR BILINEAR HILBERT TRANSFORMS AND BILINEAR MAXIMAL FUNCTIONS ASSOCIATED TO POLYNOMIALS

被引：26

作者：

Li, Xiaochun ^{[1
]}

Xiao, Lechao ^{[2
]}

机构：

[1] Univ Illinois, Dept Math, 1409 W Green St, Urbana, IL 61801 USA

[2] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2016年 / 138卷 / 04期

关键词：

OSCILLATORY INTEGRALS; SINGULAR-INTEGRALS; CURVES; OPERATORS; BOUNDS;

D O I：

10.1353/ajm.2016.0030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the bilinear Hilbert transforms and bilinear maximal functions associated to non-flat polynomial curves and obtain uniform L-r estimates for r > d-1/d, where d is the degree of the polynomial. In addition, the lower bound of r is sharp up to the end point.

引用

页码：907 / 962

页数：56

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