The Poletskii and V\"{a}is\"{a}l\"{a} inequalities for the mappings with $(p, q)$--distortion

TL;DR

This paper extends classical inequalities to a broader class of space mappings with $(p, q)$-distortion, providing new modulus inequalities that generalize known results for quasiregular mappings.

Contribution

It introduces analogues of Poletskii and V"{a}is"{a}l"{a} inequalities for mappings with $(p, q)$-distortion, expanding the theoretical framework.

Findings

Derived modulus inequalities for $(p, q)$-distorted mappings

Generalized classical inequalities to broader mapping classes

Enhanced understanding of space mappings beyond quasiregular ones

Abstract

The present paper is devoted to the study of space mappings, which are more general than quasiregular. The so--called modulus inequalities for some class of mappings are obtained. In particular, the analogues of the well--known Poletskii and V\"{a}is\"{a}l\"{a} inequalities were proved.