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

Science China Mathematics - Tập 56 - Trang 1895-1913 - 2012
Yu Liu1, JiZheng Huang2, JianFeng Dong3
1School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China
2College of Sciences, North China University of Technology, Beijing, China
3Department of Mathematics, Shanghai University, Shanghai, China

Tóm tắt

Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator T b f = bT f − T(bf) on L p , p ∈ (1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b ∈ BMO θ (X) ⊇ BMO(X). Moreover, they prove that T b is bounded from the Hardy space H 1 (X) into the weak Lebesgue space L weak 1 (X). This can be used to deal with the Schrödinger operators and Schrödinger type operators on the Euclidean space ℝ n and the sub-Laplace Schrödinger operators on the stratified Lie group $\mathbb{G}$ .

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