Dimension compression and expansion under homeomorphisms with exponentially integrable distortion

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.

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The author has been supported by the Academy of Finland project SA-1346562.

Received 23 March 2022

Received revised 25 May 2022

Accepted 13 June 2022

Published 26 October 2022