The paper continues the study of a class of holomorphic Besov spaces on bounded symmetric domains which was initiated in [18]. Several new descriptions of these Besov spaces are given in terms of weighted Bergman projections and fractional differential operators. These new characterizations are then applied to obtain results about the duality of, and Hankel operators on, weighted Bergman spaces...

We present several embedding results for 3-graded Lie algebras and KKT algebras that are generated by two homogeneous elements of degrees 1 and −1. We also propose the canonical kernel function for a “universal Bergman kernel” which extends the usual Bergman kernel on a bounded symmetric domain to a group-valued function or, in terms of formal series, to an element in the formal completion of t...

We compute the explicit formula of the Bergman kernel for a nonhomogeneous domain {(z1, z2) ∈ C2 : |z1|1 + |z2|2 < 1} for any positive integers q1 and q2. We also prove that among the domains Dp := {(z1, z2) ∈ C2 : |z1|1 + |z2|2 < 1} in C2 with p = (p1, p2) ∈ N2, the Bergman kernel is represented in terms of closed forms if and only if p = (p1, 1), (1, p2), or p = (2, 2).

Cory Hawkins,* D. Scott Wills, Odile Liboiron-Ladouceur, and Keren Bergman School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive NW, Atlanta, Georgia 30332-0250, USA Department of Electrical Engineering, Columbia University in the City of New York, 500 West 120th Street, New York, New York 10027, USA E-mail: [email protected] E-mail: ol2007@...