Cheng-Xi Li

Characterizations for quasiconformal weighted Bergman spaces

We establish characterizations of planar quasiconformal mappings in weighted Bergman spaces $A_\alpha^p(\mathbb D)$. For $p>0$ and $\alpha>-1$, our characterization involves the convergence of certain integrals involving superlevel set areas, the Hausdorff measure of boundary superlevel sets, and the averaged derivativ...