Characterization of Lipschitz Functions on Ball Banach Function Spaces

Our goal is to characterize the Lipschitz functions by ball Banach function space. We give some necessary and sufficient conditions of the boundedness of the maximal commutators, commutators of the Hardy–Littlewood maximal operators and commutators of the sharp maximal operators when the symbol b belongs to Lipschitz (Campanato) spaces. In light of the results to be obtained, some applications in ball Banach function spaces will also be presented.