The lower Q-homeomorphisms relative to a p-modulus

Abstract

The paper is devoted to the development of the theory of lower Q-homeomorphisms relative to a p-modulus in ℝⁿ, n ≥ 2. For these classes of mappings, a number of theorems on the local behavior are established, and, in particular, an analog of the famous Gehring theorem on a local Lipschitz property is proved, various theorems on estimates of distortion of the Euclidean distance are given, an estimate of the ball image measure is established, and, as a consequence, an analog of the Ikoma–Schwartz lemma is proved.