HANKEL-OPERATORS ON THE BERGMAN SPACE OF BOUNDED SYMMETRICAL DOMAINS

Let OMEGA be a bounded symmetric domain in C(n) with normalized volume measure dV. Let P be the orthogonal projection from L2(OMEGA, dV) onto the Bergman space L(a)2(OMEGA) of holomorphic functions in L2(OMEGA, dV). Let PBAR be the orthogonal projection from L2(OMEGA, dV) onto the closed subspace of antiholomorphic functions in L2(OMEGA, dV). The "little" Hankel operator h(f) with symbol f is the operator from L(a)2(OMEGA) into L2(OMEGA, dV) defined by h(f)g = PBAR(fg). We characterize the boundedness, compactness, and membership in the Schatten classes of the Hankel operators h(f) in terms of a certain integral transform of the symbol f. These characterizations are further studied in the special cases of the open unit ball and the poly-disc in C(n).