On regularity of the Berezin transform on smooth pseudoconvex domains

Berezin regularity of domains in C^n and the essential norms of Toeplitz operators

For the open unit disc $\mathbb{D}$ in the complex plane, it is well known that if $ϕ\in C(\overline{\mathbb{D}})$ then its Berezin transform $\widetildeϕ$ also belongs to $C(\overline{\mathbb{D}})$. We say that $\mathbb{D}$ is BC-regular. In this paper we study BC-regularity of some pseudoconvex domains in $\mathbb{C}^n$ and show that the boundary geometry plays an important role. We also establish a relationship between the essential norm of an operator in a natural Toeplitz subalgebra and its Berezin transform.

Berezin变换的$L^p$正则性的一个充分条件

A sufficient condition for $L^p$ regularity of the Berezin transform

本文证明了Berezin变换在$\nathbb{C}^n$的一大类域上具有$L^p$正则性，但在Hartogs三角形上缺乏$L^2$正则性。