Toeplitz operators with unbounded symbols of several complex variables ✩

In this note we construct a function ϕ in L2(Bn, dA) which is unbounded on any neighborhood of each boundary point of Bn such that Tϕ is a trace class operator on Bergman space L2a (Bn) for several complex variables. In addition, we also discuss the compactness of Toeplitz operators with L1 symbols. © 2007 Elsevier Inc. All rights reserved