GRADIENT ESTIMATES FOR THE COMMUTATOR WITH FRACTIONAL DIFFERENTIATION FOR SECOND ORDER ELLIPTIC OPERATORS  

作　　者：Wenyu TAO bnping CHEN Jili LI 陶文宇;陈艳萍;李纪黎(Department of Applied Mathematics,School of Mathematics and Physics,University of Science and Technology Beijing)

机构地区：[1]Department of Applied Mathematics,School of Mathematics and Physics,University of Science and Technology Beijing

出　　处：《Acta Mathematica Scientia》2019年第5期1255-1264,共10页数学物理学报（B辑英文版）

基　　金：supported by NSFC(11471033),NCET of China(NCET-11-0574);the Fundamental Research Funds for the Central Universities(FRF-BR-16-011A)

摘　　要：Let L=-div(A▽) be a second order divergence form elliptic operator, where A is an accretive, n×n matrix with bounded measurable complex coefficients on R^n. Let L^α/2 (0 <α< 1) denotes the fractional differential operator associated with L and (-△)^α/2b ∈ L^n/α(R^n). In this article, we prove that the commutator[b, L^α/2] is bounded from the homogenous Sobolev space Lα%2 (R^n) to L^2(R^n).Let L=-div（A▽） be a second order divergence form elliptic operator,where A is an accretive,n×n matrix with bounded measurable complex coefficients on Rn.Let Lα/2（0<α<1） denotes the fractional differential operator associated with L and（-△）α/2b∈Ln/α（Rn）.In this article,we prove that the commutator [b,Lα/2] is bounded from the homogenous Sobolev space Lα2（Rn） to L2（Rn）.

关 键 词：COMMUTATOR FRACTIONAL differentiation ELLIPTIC OPERATORS SOBOLEV space 

分 类 号：O[理学]