A remark on Carleson measures of domains in ℂⁿ

Thuc, Phung

doi:10.1090/proc/15881

A remark on Carleson measures of domains in $\mathbb {C}^{n}$
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Proc. Amer. Math. Soc. 150 (2022), 2579-2592 Request permission

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 \begin{equation*} \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}^{+}. \end{equation*}

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