Bergman spaces with small exponents

We give a complete proof of the characterization of the dual spaces of weig hted Bergman spaces A(p), p is an element of (0, 1), of a bounded symmetric domain Omega in C-n as Besov spaces of holomorphic functions (Bloch spaces ). This result was stated by K. Zhu but there is a gap in his proof. This p roblem is first solved in symmetric Siegel domains of type II and in two pa rticular homogeneous, nonsymmetric Siegel domains of type II. The required result is then obtained via a transfer principle from the realization of Om ega as a Siegel domain of type IT to Omega.