Products of Toeplitz and Hankel Operators on Fock-Sobolev Spaces

Abstract

In this paper, we investigate the boundedness of Toeplitz product $T_f{T}_g$ and Hankel product $H_f^{\ast }{H}_g$ on Fock-Sobolev space for two polynomials $f$ and $g$ in $z,\overline{z}\in {\mathbb{C}}^n$. As a result, the boundedness of Toeplitz operator $T_f$ and Hankel operator $H_f$ with the polynomial symbol $f$ in $z,\overline{z}\in {\mathbb{C}}^n$ is characterized.

13 pages