Sparse Domination and Weighted Estimates for Rough Bilinear Singular Integrals

被引：2
|
作者：
Grafakos, Loukas [1 ]
Wang, Zhidan [2 ,3 ]
Xue, Qingying [2 ]
机构：
[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA
[2] Beijing Normal Univ, Sch Math Sci, Minist Educ, Lab Math & Complex Syst, Beijing 100875, Peoples R China
[3] Nanjing Tech Univ, Sch Phys & Math Sci, Nanjing 211816, Peoples R China
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2022年 / 28卷 / 06期
基金：
国家重点研发计划;
关键词：
Sparse domination; Rough bilinear singular integrals; A(p; r); weights; WEAK-TYPE 1,1; 1; BOUNDS; OPERATORS;
D O I：
10.1007/s00041-022-09973-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let r > 4/3 and let Omega is an element of L-r (S2n-1) have vanishing integral. We show that the bilinear rough singular integral T-Omega(f, g((x) = p.v.integral(Rn)integral(Rn) Omega((y, z)/vertical bar(y, z vertical bar)/vertical bar(y, z)vertical bar(2n) f(x - y)g(x - z)dydz, satisfies a sparse bound by (p, p, p)-averages, where p is bigger than a certain number explicitly related to r and n. As a consequence we deduce certain quantitative weighted estimates for bilinear homogeneous singular integrals associated with rough homogeneous kernels.
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页数：27
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