On absolute continuity for mappings, distorting moduli of cylinders

TL;DR

This paper investigates mappings that distort moduli of cylinders in a space, establishing their absolute continuity on lines by relating modulus distortion to a locally integrable function.

Contribution

It introduces conditions under which mappings satisfying a modular inequality exhibit absolute continuity on lines, extending understanding of modulus distortion effects.

Findings

Mappings satisfying the modular inequality are absolutely continuous on lines.

Distortion of modulus is controlled by an integral involving a locally integrable function.

The paper generalizes previous results on modulus distortion and absolute continuity.

Abstract

In the present paper, mappings satisfying one modular inequality with respect to cylinders in a space, are considered. Distorting of modulus is majorized by an integral which depends from some locally integrable function. The result on absolute continuity on lines of the functions mentioned above is proved