Let T be an anisotropic Calderón-Zygmund operator andφ:R^n×[0,∞)→[0,∞)be an anisotropic Musielak-Orlicz function withφ(x,·)being an Orlicz function andφ(·,t)being a Muckenhoupt A∞(A)weight.I...Let T be an anisotropic Calderón-Zygmund operator andφ:R^n×[0,∞)→[0,∞)be an anisotropic Musielak-Orlicz function withφ(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(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^1ω(R^n,A)to weighted Lebesgue space L^1ω(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.展开更多
基金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)the third author is supported by the the National Natural Science Foundation of China(11671414).
文摘Let T be an anisotropic Calderón-Zygmund operator andφ:R^n×[0,∞)→[0,∞)be an anisotropic Musielak-Orlicz function withφ(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(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^1ω(R^n,A)to weighted Lebesgue space L^1ω(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.
