Embedding theorems for Bergman spaces in quasiconformal balls (Q804745)

Embedding theorems for Bergman spaces of analytic, harmonic or quasiregular functions on the unit disc in \({\mathbb{C}}\) or on the unit ball in \(R^ n\) have been studied by V. L. Oleinik, B. S. Pavlov, D. Stegenga, D. Luecking, C. A. Nolder and others. The present paper extends some earlier results of the first author in two respects (1) the domains are more general (2) the functions are more general. Among the classes of domains considered are quasiconformal balls and also domains satisfying a singular integral condition \(\int_{G}d(x,\partial G)^{- \gamma}dm<\infty\) for some \(\gamma >0\).