Toeplitz operators with essentially radial symbols (Q417260)

Summary: For Toeplitz operators with radial symbols on the disk, there are important results that characterize boundedness, compactness, and its relation to the Berezin transform. The notion of essentially radial symbol is a natural extension, in the context of multiply connected domains, of the notion of radial symbol on the disk. In this paper, we analyze the relationship between the boundary behavior of the Berezin transform and the compactness of \(T_{\phi}\) when \(\phi \in L^2(\Omega)\) is essentially radial and \(\Omega\) is a multiply connected domain.