Necessary and sufficient conditions for boundedness of commutators of maximal function on the $ p $-adic vector spaces

Abstract

<abstract><p>In this paper, we first show that the $ p $-adic version of maximal function $ \mathcal{M}_{L\log L}^{p} $ is equivalent to the maximal function $ \mathcal{M}^{p}(\mathcal{M}^{p}) $ and that the class of functions for which the maximal commutators and the commutator with the $ p $-adic version of maximal function or the maximal sharp function are bounded on the $ p $-adic vector spaces are characterized and proved to be the same. Moreover, new pointwise estimates for these operators are proved.</p></abstract>