THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS

doi:10.1007/s10473-020-104-1

Abstract

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 ∈ BMO_w(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 H_w¹(Rⁿ, A) to weighted Lebesgue space L_w¹(Rⁿ) and when b ∈ BMO(Rⁿ) (bounded mean oscillation space), the commutator [b, T] is bounded on Musielak-Orlicz space L^φ(Rⁿ), which are extensions of the isotropic setting.

Key words: expansive dilation, Muckenhoupt weight, weighted Hardy space, Calderón-Zygmund operator, commutator

CLC Number:

42B35

Jinxia LI, Baode LI, Jianxun HE. THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS[J].Acta mathematica scientia,Series B, 2020, 40(1): 45-58.

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