Hardy spaces and Szegő projection on quotient domains

Abstract

The Hardy spaces are defined on the quotient domain of a bounded complete Reinhardt domain by a finite subgroup of $U(n)$. The Szegő projection on the quotient domain can be studied by lifting to the covering space. This setting builds on the solution of a boundary value problem for holomorphic functions. In particular, when the covering space is either the polydisc or the unit ball in ${\mathbb{C}}^n$, the boundary value problem can be solved. Applying this theory in ${\mathbb{C}}^2$, we further obtain sharp results on the $L^p$ regularity of the Szegő projection on the symmetrized bidisc, generalized Thullen domains, and the minimal ball.

33 pages