Compactness of Toeplitz operators with continuous symbols on pseudoconvex domains in ${\mathbb{C}}^n$

Let $\mathrm{\Omega }$ be a bounded pseudoconvex domain in ${\mathbb{C}}^n$ with Lipschitz boundary and $\phi$ be a continuous function on $\bar{\mathrm{\Omega }}$. We show that the Toeplitz operator $T_{\phi }$ with symbol $\phi$ is compact on the weighted Bergman space if and only if $\phi$ vanishes on the boundary of $\mathrm{\Omega }$. We also show that compactness of the Toeplitz operator $T_{\phi }^{p,q}$ on $\bar{\mathrm{\partial }}$-closed $(p,q)$-forms for $0\le p\le n$ and $q\ge 1$ is equivalent to $\phi =0$ on $\mathrm{\Omega }$.