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On a Theorem of Hayman Concerning Quasi-Bounded Functions
Published online by Cambridge University Press: 20 November 2018
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If f(z) is regular in |z| < 1, the expression
is called the characteristic of f(z). This is the notation of Nevanlinna (4) for the special case of regular functions; in this note it will not be necessary to discuss meromorphic functions. If m(r,f) is bounded for 0 < r < 1, then f(z) is called quasi-bounded in |z| < 1. In particular, every bounded function is quasibounded. The class Q of quasi-bounded functions is important because, for instance, a “Fatou theorem” holds for such functions (4, p. 134).
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- Copyright © Canadian Mathematical Society 1959
References
1.
Hayman, W. K., On Nevanlinna's second theorem and extensions, Rend. Circ. Mat. Palermo, Ser. II, II/ (1953).Google Scholar
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Kennedy, P. B., A property of bounded tegular functions, Proc. Roy. Irish Acad., 60, sec. A, no. 2 (1959).Google Scholar
4.
Nevanlinna, R., Le Théorème de Picard-Borel et la Théorie des Fonctions Méromorphes (Paris, 1929).Google Scholar
5.
Specht, E. J., Estimates on the mapping function and its derivatives in conformai mapping of nearly circular regions, Trans. Amer. Math. Soc, 71 (1951), 183–96.Google Scholar
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