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Abstract. We define locally convex spaces LW and HW consisting of measurable and holomorphic functions in the unit ball, respectively, with the topology given by a family of weighted-sup seminorms. We prove that the Bergman projection is a continuous map from LW onto HW . These are the smallest spaces having this property. We investigate the topological and algebraic properties of HW .

This paper concerns certain geometric aspects of function theory on smoothly bounded convex domains of finite type in C n . Specifically, we prove the Carleson-Hörmander inequality for this class of domains and provide examples of Carleson measures improving a known result concerning such measures associated to bounded holomorphic functions.