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arXiv · 2009.09252

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

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

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Phung Trong Thuc. 2020-09-19. A remark on Carleson measures of domains in $\mathbb{C}^{n}$. https://arxiv.org/abs/2009.09252

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