Abstract
In this paper we study the problem of the boundedness and compactness of the Toeplitz operator Tϕ on L2a(Ω), where Ω is a multiply-connected domain and ϕ is not bounded. We find a necessary and sufficient condition when the symbol is BMO. For this class we also show that the vanishing at the boundary of the Berezin transform is a necessary and sufficient condition for compactness. The same characterization is shown to hold when we analyze operators which are finite sums of finite products of Toeplitz operators with unbounded symbols.
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