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

作　　者：Wenyu Tao Yanping Chen Yayuan Xiao Liwei Wang 

机构地区：[1]School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,China [2]Department of Mathematical Sciences,Ball State University,Muncie,IN 47306,USA [3]School of Mathematics and Physics,Anhui Polytechnic University,Wuhu 241000,China

出　　处：《Science China Mathematics》2020年第3期575-594,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 11471033);Program for New Century Excellent Talents in University of China (Grant No. NCET-11-0574);the Fundamental Research Funds for the Central Universities (Grant No. FRF-BR-17-001B);the Fundamental Research Funds for Doctoral Candidate of University of Science and Technology Beijing (Grant No. FRF-BR-17018)

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,L1/2]of the Kato square root L1/2 and b with ▽b∈Ln（Rn）（n> 2）,is bounded from the homogenous Sobolev space L1p（Rn） to Lp（Rn）（p-（L） <p<p+（L））.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,L1/2]of the Kato square root L1/2 and b with ▽b∈Ln(Rn)(n> 2),is bounded from the homogenous Sobolev space L1p(Rn) to Lp(Rn)(p-(L)

关 键 词：COMMUTATOR Kato square root elliptic operators Sobolev space 

分 类 号：O175[理学—数学]