On the continuity of discrete maximal operators in Sobolev spaces

Abstract

Abstract. We investigate the continuity of discrete maximal operators in Sobolev spaceA counterexample is given as well as it is shown that the continuity follows under certain sufficient assumptions. Especially, our research verifies that for the continuity in Sobolev spaces the role of the partition of the unity used in the construction of the maximal operator is very delicate.