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We obtain sharp ranges of $L^p$-boundedness for domains in a wide class of Reinhardt domains representable as sub-level sets of monomials, by expressing them as quotients of simpler domains. We prove a general transformation law relating $L^p$-boundedness on a domain and its quotient by a finite group. The range of $p$ for which the Bergman projection is $L^p$-bounded on our class of Reinhardt domains is found to shrink as the complexity of the domain increases., New main theorem and two new co-authors. The new results are applicable to a much more general class of domains

We compute the exact norms of the Leray transforms for a family S β of unbounded hypersurfaces in two complex dimensions. The S β generalize the Heisenberg group, and provide local projective approximations to any smooth, strongly C -convex hypersurface S to two orders of tangency. This work is then examined in the context of projective dual CR-structures and the corresponding pair of canonical dual Hardy spaces associated to S , leading to a universal description of the Leray transform and a factorization of the transform through orthogonal projection onto the conjugate dual Hardy space.

Expected duality and approximation properties are shown to fail on Bergman spaces of domains in C n , via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are proved. Such operators are constructed on generalized Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of Laurent series of Bergman functions is shown. This extends a classical result on Hardy spaces of the unit disc.