Lower Semicontinuity of Distortion Coefficients for Homeomorphisms of Bounded (1, σ)-Weighted (q, p)-Distortion on Carnot Groups

Abstract

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