Hardy and Bergman spaces with applications

Abstract

The present work addresses issues of duality and approximation in Bergman spaces, based on recent results by Chakrabarti, Edholm, and McNeal (2019), and includes a complementary study on Hardy spaces in the unit disk. Three central problems are explored: the characterization of the dual space, the approximation by well-behaved holomorphic functions, and the construction of the closest analytic functions in L^p. The study focuses on bounded domains in \C^n with special emphasis on Reinhardt domains, particularly the generalized Hartogs triangles where sub-Bergman projections arise, extending the classical theory.