Modified Bergman spaces on the unit ball of Cⁿ and applications

Abstract In this paper, we introduce new spaces Aᵖ₀, ₁ (Bₙ) of holomorphic functions on the unit ball B₍ of C^n generalizing the classical Bergman spaces. We start by giving some properties of these spaces and the determination of the reproducing kernel in the case p=2, then we study the boundedness of the Bergman projections. Using the Berezin transform, a type of Bergman-Poincar\'e metric with an application on the space of bounded mean oscillation functions are given at the end of the paper. 2010 Mathematics Subject Classification. 47G10, 32A25, 32A36, 32A37.