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.
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页码：907 / 962
页数：56
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