Analytic properties of Besov spaces via Bergman projections

Abstract

We consider two-parameter Besov spaces of holomorphic functions on the unit ball of CN: We obtain various exclusions between Besov spaces of di®erent parameters using gap series. We estimate the growth near the boundary and the growth of Taylor coe±cients of functions in these spaces. We ¯nd the unique function with maximum value at each point of the ball in each Besov space. We base our proofs on Bergman projections and imbeddings between Lebesgue classes and Besov spaces. Special cases apply to the Hardy space H2, the Arveson space, the Dirichlet space, and the Bloch space.