Commutators of Calderón-Zygmund operators related to admissible functions on spaces of homogeneous type and applications to Schrdinger operators

作     者：LIU Yu HUANG JiZheng DONG JianFeng 

作者机构：School of Mathematics and PhysicsUniversity of Science and Technology Beijing College of SciencesNorth China University of Technology Department of MathematicsShanghai University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第9期

页      面：1895-1913页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China (Grant Nos. 10901018 and 11001002) the Shanghai Leading Academic Discipline Project (Grant No. J50101) the Fundamental Research Funds for the Central Universities 

主　　题：commutator spaces of homogeneous type stratified Lie groups admissible function Hardy space reverse Ho¨lder inequality Riesz transform Schr¨odinger operators 

摘      要：Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈BMOθ(X)BMO(X). Moreover, they prove that Tb is bounded from the Hardy space H1ρ(X) into the weak Lebesgue space L1weak(X). This can be used to deal with the Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.