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 $$\mathbb{H}{k}:=\left{ \left(z{1},z_{2}\right)\in\mathbb{C}^{2}:\left|z_{1}\right|^{k}<\left|z_{2}\right|<1\right},\;k\in\mathbb{Z}^{+}.$$