Abstract
We show that the description of Carleson measures on the Bergman space of analytic functions on a finitely connected domain G with a power weight is similar to that for the unit disk iff the complement \(\overline {\mathbb{C}} \backslash G\) is an unbounded set without isolated points. In the general case, the complement of such a domain G must be uniformly perfect. Bibliography: 20 titles.
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Oleinik, V.L. Carleson Measures and Uniformly Perfect Sets. Journal of Mathematical Sciences 107, 4029–4037 (2001). https://doi.org/10.1023/A:1012436632556
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DOI: https://doi.org/10.1023/A:1012436632556