Rotation bounds for H\"older continuous homeomorphisms with integrable distortion

We obtain sharp rotation bounds for the subclass of homeomorphisms $f:\mathbb{C}\to\mathbb{C}$ of finite distortion which have distortion function in $L^p_{loc}$, $p>1$, and for which a H\"older continuous inverse is available. The interest in this class is partially motivated by examples arising from fluid mechanics. Our rotation bounds hereby presented improve the existing ones, for which the H\"older continuity is not assumed. We also present examples proving sharpness.