Boundedness and Compactness for the Commutator of the ω-Type Calderón-Zygmund Operator on Lorentz Space

In this paper, the authors consider the ω -type Calderón-Zygmund operator T ω and the commutator [ b, T ω ] generated by a symbol function b on the Lorentz space L p,r ( X ) over the homogeneous space ( X, d, μ ). The boundedness and the compactness of the commutator [ b, T ω ] on Lorentz space L p,r ( X ) are founded for any p ∈ (1, ∞) and r ∈ [1, ∞).