CHARACTERIZATIONS OF CERTAIN CLASSES OF HANKEL-OPERATORS ON THE BERGMAN SPACES OF THE UNIT DISK

Let f be an integrable function on the unit disk. The Hankel operator Hf is densely defined on the Bergman space Ap by Hfg = fg - P(fg), where g is a bounded analytic function and P is the Bergman projection (orthogonal projection from L2 to A2) extended to L1 via its integral formula. In this paper, the functions f for which Hf extends to a bounded operator from Ap to Lp are characterized, 1 < p < ∞. Also characterized are the functions f for which Hf extends to a compact or Schatten class operator on A2. The proofs can be extended to handle any smoothly bounded domain in C in place of the unit disk. © 1992.