  In this work we explore the theme of $L^p$-boundedness of Bergman projections
of domains that can be covered, in the sense of ramified coverings, by "nice"
domains (e.g. strictly pseudoconvex domains with real analytic boundary). In
particular, we focus on two-dimensional normal ramified coverings whose
covering group is a finite unitary reflection group. In an infinite family of
examples we are able to prove $L^p$-boundedness of the Bergman projection for
every $p\in(1,\infty)$.
