Products of Toeplitz and Hankel Operators on Fock-Sobolev Spaces

TL;DR

This paper characterizes the boundedness of Toeplitz and Hankel operators with polynomial symbols on Fock-Sobolev spaces, focusing on products of these operators and their boundedness conditions.

Contribution

It provides new criteria for the boundedness of Toeplitz and Hankel operator products with polynomial symbols on Fock-Sobolev spaces.

Findings

Boundedness conditions for Toeplitz products $T_f T_g$

Boundedness conditions for Hankel products $H_f^* H_g$

Characterization of bounded Toeplitz and Hankel operators with polynomial symbols

Abstract

In this paper, we investigate the boundedness of Toeplitz product $T_{f}T_{g}$ and Hankel product $H_{f}^{*} H_{g}$ 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.