  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.
