A remark on Carleson measures of domains in ${\mathbb{C}}^n$

Abstract

We provide characterizations of Carleson measures on a certain class of bounded pseudoconvex domains. An example of a vanishing Carleson measure whose Berezin transform does not vanish on the boundary is given in the class of the Hartogs triangles $${\mathbb{H}}_k:=\left\{\left(z_1,z_2\right)\in {\mathbb{C}}^2:{\left|z_1\right|}^k<\left|z_2\right|<1\right\},k\in {\mathbb{Z}}^{+}.$$

References in corpus (1)

• Compactness of the $\bar{\partial }$-Neumann problem on domains with bounded intrinsic geometry