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 Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.
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 Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.
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
关键词
D-空间
薛定谔
运营商
换向器
卡尔
同质化
HARDY空间
应用
commutator, spaces of homogeneous type, stratified Lie groups, admissible function, Hardy space, reverse Ho¨lder inequality, Riesz transform, Schr¨odinger operators
