THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERóN-ZYGMUND OPERATORS

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 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∈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 Hω1(Rn,A) to weighted Lebesgue space Lω1(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.