Compact Toeplitz operators on parabolic Bergman spaces

Abstract

Parabolic Bergman space $\berg[p]$ is a Banach space of all $p$-th integrable solutions of a parabolic equation $(\partial/\partial t + (-\Delta)^{\alpha})u = 0$ on the upper half space, where $0<\alpha\leq1$ and $1\leq p<\infty$. In this note, we consider the Toeplitz operator from $\berg[p]$ to $\berg[q]$ where $p\leq q$, and discuss the condition that it be compact.