Dimension compression and expansion under homeomorphisms with exponentially integrable distortion

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.