Dimension compression and expansion under homeomorphisms with exponentially integrable distortion

TL;DR

This paper advances the understanding of how homeomorphisms with exponentially integrable distortion affect dimension compression and expansion, introducing new estimates for multifractal spectra and demonstrating sharpness through examples.

Contribution

It provides improved bounds for dimension change under such homeomorphisms and introduces estimates for compression and rotational multifractal spectra.

Findings

New bounds for dimension compression and expansion under exponentially integrable distortion.

Introduction of estimates for compression and rotational multifractal spectra.

Construction of examples demonstrating the sharpness of the bounds.

Abstract

We improve both dimension compression and expansion bounds for homeomorphisms with $p$-exponentially integrable distortion. To the first direction we also introduce estimates for the compression multifractal spectra, which will be used to estimate compression of dimension, and for the rotational multifractal spectra. For establishing the expansion case we use the multifractal spectra of the inverse mapping and construct examples proving sharpness.