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

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Abstract

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 ρ (X) into the weak Lebesgue space L 1weak (X). This can be used to deal with the Schrödinger operators and Schrödinger type operators on the Euclidean space ℝn and the sub-Laplace Schrödinger operators on the stratified Lie group \(\mathbb{G}\).

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Yu Liu

  2. College of Sciences, North China University of Technology, Beijing, 100144, China

    JiZheng Huang

  3. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    JianFeng Dong

Authors
  1. Yu Liu
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  2. JiZheng Huang
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  3. JianFeng Dong
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Correspondence to Yu Liu.

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Liu, Y., Huang, J. & Dong, J. Commutators of Calderón-Zygmund operators related to admissible functions on spaces of homogeneous type and applications to Schrödinger operators. Sci. China Math. 56, 1895–1913 (2013). https://doi.org/10.1007/s11425-012-4551-3

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  • DOI: https://doi.org/10.1007/s11425-012-4551-3

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