On the regularity and continuity of the multilinear fractional strong maximal operators

Abstract

AbstractLet , , and denote the family of all rectangles in with sides parallel to the axes. The main purpose of this paper is to study the regularity and continuity properties of the multilinear fractional strong maximal operators associated with rectangles which covers the multilinear strong maximal operator , corresponding to the critical index . Boundedness and continuity for the map are proved, provided that , and . As an application of the above boundedness result, the q‐quasicontinuity for is established. In addition, we also prove that a vector function with each implies almost everywhere approximately differentiability of when , which is stronger than the best result known for .