On convergence analysis of space homeomorphisms

Abstract

Various theorems on convergence of general spatial homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring Q-homeomorphisms are obtained. In particular, it is established that a family of all ring Q-homeomorphisms f in ℝn fixing two points is compact provided that the function Q is of finite mean oscillation. The corresponding applications have been given to mappings in the Sobolev classes Wloc1,p for the case p > n − 1.