Toeplitz operators on pluriharmonic Fock spaces

Abstract

In this paper, we study Toeplitz operators with a positive symbol on pluriharmonic Fock spaces over ${\mathbb{C}}^n.$ We characterize the conditions under which the Toeplitz operator $T_{\hat{I}}¼$ is bounded, compact, or belongs to the Schatten class $S_1$. Furthermore, we give a necessary condition for a Toeplitz operator to belong to $S_p$ for $p\ge 1,$ and under an additional assumption, we prove the sufficiency of the condition.

11 pages