Endpoint Regularity of Multisublinear Fractional Maximal Functions

In this paper we investigate the endpoint regularity properties of the multisublinear fractional maximal operators, which include the multisublinear Hardy–Littlewood maximal operator. We obtain some new bounds for the derivative of the one-dimensional multisublinear fractional maximal operators acting on the vector-valued function $\overrightarrow{f}=({{f}_{1}},...,{{f}_{m}})$ with all ${{f}_{j}}$ being $BV$ -functions.