Joint rotational and stretching multifractal spectra of mappings with integrable distortion

Abstract

We establish bounds for both the stretching and the rotational multifractal spectra of planar homeomorphic mappings with $p$-integrable distortion. Moreover, we show that these bounds are sharp by presenting extremal examples of homeomorphic mappings with $p$-integrable distortion that attain the optimal stretching and rotation simultaneously, which additionally leads to the sharp bound for the joint rotational and stretching multifractal spectra. Finally, we will use the stretching multifractal spectra to obtain the sharp area contraction for homeomorphic mappings with $p$-integrable distortion.