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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.
Amor et al. (Tue,) studied this question.