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