Compact operators on the Bergman space of multiply-connected domains

Abstract

If Ω is a smoothly bounded multiply-connected domain in the complex plane and A = ∑j=1m= ∏k=1 Tφj,k, where φj,k ∈ L∞(Ω, dv) we show that A is compact if and only if its Berezin transform vanishes at the boundary. © 2000 American Mathematical Society.