On the continuity of some classes and subclasses of maps with an s-averaged characteristic

Abstract

. According to the well-known theorem of S. L. Sobolev, if 𝐺 is a bounded domain of Euclidean space and a function is a function having the first generalized derivatives summable with degree 𝑝 , then it is continuous in 𝐺 . If 1 < 𝑝 (cid:54) 𝑛 this property, generally speaking, may not be. In this paper, we find the necessary conditions under which some classes and subclasses of maps with an 𝑠 -averaged characteristic will be continuous. Examples of subclasses of such mappings with the above properties are given in our papers.