Endpoint regularity of discrete multilinear maximal and minimal operators

We introduce two discrete multilinear maximal and minimal operators associated to the function f, which cover the classical discrete multilinear maximal and minimal operators and their fractional variants. Under a more restrictive condition on f, we establish some new variation boundedness and continuity of the above operators, which is new and interesting even in the linear case. It should be pointed out that the main results we obtain not only extend and improve some known ones in the maximal setting, but also supplement some new results in the minimal setting.