This paper studies the boundary behavior of the Berezin transform on the C∗-algebra generated by the analytic Toeplitz operators on the Bergman space.

We show that the Bergman projection does not preserve smoothness of functions in some pseudoconvex domains in the space of two complex variables.

It is shown that the formula for the Möbius pseudodistance for the annulus yields better estimates than previously known for the constant in the Bergman space maximum principle.

This paper presents a rigidity theorem for infinite dimensional Bergman spaces of hyperbolic Riemann surfaces, which states that the Bergman space A1(M), for such a Riemann surface M , is isomorphic to the Banach space of summable sequence, l1. This implies that whenever M and N are Riemann surfaces which are not analytically finite, and in particular are not necessarily homeomorphic, then A1(M...

On the setting of Siegel upper half-space we study spaces bounded and vanishing mean oscillations which are defined in terms Berezin transform, use them to characterize compact Hankel operators on Bergman space. When symbols specialized be holomorphic, its corresponding Bloch space half-space.