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The Boundedness for Commutators of Anisotropic Calderón-Zygmund Operators

Authors
  • Li, Jinxia1
  • Li, Baode2
  • He, Jianxun1
  • 1 Guangzhou University, Guangzhou, 510006, China , Guangzhou (China)
  • 2 Xinjiang University, Urumqi, 830046, China , Urumqi (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jan 20, 2020
Volume
40
Issue
1
Pages
45–58
Identifiers
DOI: 10.1007/s10473-020-0104-1
Source
Springer Nature
Keywords
License
Yellow

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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