A short proof of the Cima-Wogen 𝐿(𝑓)=𝑐𝑖𝑟𝑐𝑙𝑒 theorem

Antonino, José A.; Romaguera, Salvador

doi:10.1090/S0002-9939-1984-0759659-2

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A short proof of the Cima-Wogen $L(f)=\textrm {circle}$ theorem
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by José A. Antonino and Salvador Romaguera PDF

Proc. Amer. Math. Soc. 92 (1984), 391-392 Request permission

Abstract:

In [1] Cima and Wogen showed that if $f \in$ ball ${B_0}$ and $L(f)$ contains a circle $\gamma$, then $\gamma = L(f)$. This note presents a new and straightforward proof of Cima and Wogen’s theorem.

References

Joseph A. Cima and Warren R. Wogen, Extreme points of the unit ball of the Bloch space ${\cal B}_{0}$, Michigan Math. J. 25 (1978), no. 2, 213–222. MR 486558
Karl-Joachim Wirths, On holomorphic functions satisfying $\,f(z)(1-z^{2})\leq 1$ in the unit disc, Proc. Amer. Math. Soc. 85 (1982), no. 1, 19–23. MR 647889, DOI 10.1090/S0002-9939-1982-0647889-8