Averaged derivatives and reverse inequalities in quasiregular Bergman spaces

We study weighted Bergman spaces of quasiregular mappings on the unit ball in $\mathbb{R}^n$, with weight $(1-|x|)^α$, $α>-1$. For every fixed distortion bound $K\ge1$ and every $p>0$, we characterize Bergman integrability by averaged derivatives. We also give geometric conditions under which integr