Toeplitz operators and Carleson measures on parabolic Bergman spaces

Abstract

Let $\boldsymbol b^p_\alpha$ be the parabolic Bergman space, which is the Banach space of all $L^p$-solutions of the parabolic equation $(\partial/\partial t + (-\Delta)^{\alpha})u = 0$ on the upper half space $\boldsymbol R^{n+1}_+$ with $0 < \alpha \leq 1$. We discuss the relation of Toeplitz operators to Carleson measures.