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

来源：Science China Mathematics, 2013, 56(09): 1895-1913.

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

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.

• 单位
  上海大学; 北京科技大学