L~p-gradient estimates for the commutators of the Kato square roots of second-order elliptic operators on R~n

被引：0

作者：

Wenyu Tao ^{[1
]}

Yanping Chen ^{[1
]}

Yayuan Xiao ^{[2
]}

Liwei Wang ^{[1
,3
]}

机构：

[1] School of Mathematics and Physics, University of Science and Technology Beijing

[2] School of Mathematics and Physics, Anhui Polytechnic University

[3] Department of Mathematical Sciences, Ball State University

来源：

ScienceChina(Mathematics) | 2020年 / 63卷 / 03期

基金：

中国国家自然科学基金; 中央高校基本科研业务费专项资金资助;

关键词：

commutator; Kato square root; elliptic operators; Sobolev space;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

Let L=-div(A▽) be a second-order divergent-form elliptic operator,where A is an accretive n×n matrix with bounded and measurable complex coefficients on Herein,we prove that the commutator [b,L]of the Kato square root Land b with ▽b∈L~n(R~n)(n> 2),is bounded from the homogenous Sobolev space L~p(R~n) to L~p(R~n)(p-(L) <p<p+(L)).

引用

页码：575 / 594

页数：20

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