THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERóN-ZYGMUND OPERATORS

更新时间:2023-05-28

【摘要】Let T be an anisotropic Calderón-Zygmund operator and φ:R~n×[0,∞)→[0,∞) be an anisotropic Musielak-Orlicz function with φ(x,·) being an Orlicz function andφ(·,t) being a Muckenhoupt A_∞(A) weight.In this paper,our goal is to study two boundedness theorems for commutators of anisotropic Calderon-Zygmund operators.Precisely,when b∈BMO_w(R~n,A)(a proper subspace of anisotropic bounded mean oscillation space BMO(R~n,A)),the commutator [b,T] is bounded from anisotropic weighted Hardy space H_ω~1(R~n,A) to weighted Lebesgue space L_ω~1(R~n) and when b∈BMO(R~n)(bounded mean oscillation space),the commutator [b,T] is bounded on Musielak-Orlicz space L~φ(R~n),which are extensions of the isotropic setting.

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