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Proceedings of the American Mathematical Society

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A theorem of Beurling and Tsuji is best possible


Author: Shinji Yamashita
Journal: Proc. Amer. Math. Soc. 72 (1978), 286-288
MSC: Primary 30D40
MathSciNet review: 507324
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Abstract: We shall show that Beurling-Tsuji's theorem (see Theorem A) is, in a sense, best possible. For each pair $ a, b \in (0, + \infty )$ there exists a function f holomorphic in $ \{ \vert z\vert < 1\} $ such that the Euclidean area of the Riemannian image of each non-Euclidean disk of non-Euclidean radius a, is bounded by b, and such that f has finite angular limit nowhere on the unit circle.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0507324-6
Article copyright: © Copyright 1978 American Mathematical Society