Hankel Operators on the Bergman Space of Bounded Symmetric Domains

Let ii be a bounded symmetric domain in C with normalized 2 volume measure dV . Let P be the orthogonal projection from L (il, dV) 2 2 onto the Bergman space La(Q) of holomorphic functions in L (ii, dV). Let P be the orthogonal projection from L (ii, dV) onto the closed subspace of antiholomorphic functions in L (ii, dV). The "little" Hankel operator h, with symbol / is the operator from La(Ci) into L (Çl,dV) defined by hß = P{fg) ■ We characterize the boundedness, compactness, and membership in the Schatten classes of the Hankel operators h y in terms of a certain integral transform of the symbol /. These characterizations are further studied in the special cases of the open unit ball and the poly-disc in C" .