Improved bound for the bilinear Bochner-Riesz operator

被引：11

作者：

Jeong, Eunhee ^{[1
]}

Lee, Sanghyuk ^{[1
]}

Vargas, Ana ^{[2
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[2] Univ Autonoma Madrid, Dept Math, E-28049 Madrid, Spain

来源：

MATHEMATISCHE ANNALEN | 2018年 / 372卷 / 1-2期

关键词：

OSCILLATORY INTEGRALS; RESTRICTION; MULTIPLIERS; BOUNDEDNESS;

D O I：

10.1007/s00208-018-1696-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study L-p x L-q -> L-r bounds for the bilinear Bochner- Riesz operator B-alpha, alpha > 0 in R-d, d >= 2, which is defined by B-alpha (f, g) = integral integral(e2 pi ix.(xi+n))(RdxRd)(1-vertical bar xi vertical bar(2)-vertical bar eta vertical bar(2))(alpha)+(f) over cap(xi)(g) over cap(eta)d xi d eta. We make use of a decomposition which relates the estimates for Ba to the square function estimates for the classical Bochner-Riesz operators. In consequence, we significantly improve the previously known bounds.

引用

页码：581 / 609

页数：29

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