English

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

Complex Variables 2020-09-22 v1

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 Hk:={(z1,z2)C2:z1k<z2<1},  kZ+.\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}^{+}.

Keywords

Cite

@article{arxiv.2009.09252,
  title  = {A remark on Carleson measures of domains in $\mathbb{C}^{n}$},
  author = {Phung Trong Thuc},
  journal= {arXiv preprint arXiv:2009.09252},
  year   = {2020}
}