Lower semicontinuity of distortion coefficients for homeomorphisms of bounded (1, \sigma )-weighted (q, p)-distortion on Carnot groups

Abstract

In this paper we study the locally uniform convergence of homeomorphisms with bounded (1,σ)-weighted (q,p)-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded (1,σ)-weighted (q,p)-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.