Boundedness and compactness characterizations of non-convolution type Calderón-Zygmund commutators on ball Banach function spaces

Let X be a ball Banach function space on mathbb R^n and let T be a non-convolutional Calderón-Zygmund operator with the kernel K. We are devoted to studying the characterization of the boundedness and compactness of the commutator [b,~T] on ball Banach function spaces. Under the 假设 that the Hardy-Littlewood maximal operator mathcalMis bounded on both X and its associate space X', we introduce a new class of non-degenerate 条件 for the kernel K. Based on this, we prove that the commutator [b,T] is bounded on X if and only if b∈<roman>BMO</roman>(mathbb R^n and that [b,T] is compact on X if and only if b∈<roman>CMO</roman>(mathbb R^n. As applications, we obtain the characterizations of the boundedness as well as the compactness of both the Cauchy integral commutator and the Beurling-Ahlfors commutator on weighted Lebesgue spaces, Morrey spaces, mixed-norm Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces, and Orlicz-slice spaces.