Dual Toeplitz Operators on the Orthogonal Complement of the Fock–Sobolev Space

Abstract

In this paper, we consider the dual Toeplitz operators on the orthogonal complement of the Fock–Sobolev space and characterize their boundedness and compactness. It turns out that the dual Toeplitz operator S f is bounded if and only if f ∈ L ∞ , and S f = f ∞ . We also obtain that the dual Toeplitz operator with L ∞ symbol on orthogonal complement of the Fock–Sobolev space is compact if and only if the corresponding symbol is equal to zero almost everywhere.