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Let 0 <n, M_ be the fractional maximal operator, M^ be the sharp maximal operator and b be the locally integrable function. Denote by b, M_ and b, M^ be the commutators of the fractional maximal operator M_ and the sharp maximal operator M^. In this paper, we show some necessary and sufficient conditions for the boundedness of the commutators b, M_ and b, M^ on slice spaces when the function b is the Lipschitz function, by which some new characterizations of the non-negative Lipschitz function are obtained
Yang et al. (Thu,) studied this question.