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The Boundedness for Commutators of Anisotropic Calderón-Zygmund Operators

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Abstract

Let T be an anisotropic Calderón-Zygmund operator and φ : ℝn × [0, ∞) → [0, ∞) be an anisotropic Musielak-Orlicz function with φ(x, ·) being an Orlicz function and φ(·,t) being a Muckenhoupt A∞ (A) weight. In this paper, our goal is to study two boundedness theorems for commutators of anisotropic Calderón-Zygmund operators. Precisely, when b ∈ BMOw(ℝn, A) (a proper subspace of anisotropic bounded mean oscillation space BMO(ℝn, A)), the commutator [b, T] is bounded from anisotropic weighted Hardy space Hl(ℝn, A) to weighted Lebesgue space Lw1 (ℝn) and when b ∈ BMO(ℝn) (bounded mean oscillation space), the commutator [b, T] is bounded on Musielak-Orlicz space Lφ(ℝn), which are extensions of the isotropic setting.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China

    Jinxia Li  (李金霞) & Jianxun He  (何建勋)

  2. College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, China

    Baode Li  (李宝德)

Authors
  1. Jinxia Li  (李金霞)
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  2. Baode Li  (李宝德)
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  3. Jianxun He  (何建勋)
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Correspondence to Jinxia Li  (李金霞).

Additional information

The first author was supported by the “Basic Innovation” Program of Graduate Students of Guangzhou University (2018GDJC-D01); the second author is supported by the National Natural Science Foundation of China (11861062, 11661075 and 11561065) and the third author is supported by the the National Natural Science Foundation of China (11671414)

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Li, J., Li, B. & He, J. The Boundedness for Commutators of Anisotropic Calderón-Zygmund Operators. Acta Math Sci 40, 45–58 (2020). https://doi.org/10.1007/s10473-020-0104-1

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  • DOI: https://doi.org/10.1007/s10473-020-0104-1

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