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.

Toeplitz Operators on Harmonic Fock Spaces with Radial Symbols

“…The concept and properties of Fock space have been improved and generalized in many various different directions by several authors; for more details, see, e.g., [1][2][3][4] and the references therein.…”

“…For example, in the paper [2], Chen et alia considered the Toeplitz operator T a in vector-valued generalized Fock spaces. In the paper [4], He and Wu characterized dual Toeplitz operators in the orthogonal complement of Fock-Sobolev spaces.…”