Hostname: page-component-65f69f4695-2qqrh Total loading time: 0 Render date: 2025-06-29T12:18:13.232Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Theorem of Hayman Concerning Quasi-Bounded Functions

Published online by Cambridge University Press:  20 November 2018

P. B. Kennedy
P. B. Kennedy*
Affiliation:
University College, Cork, Ireland
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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).

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 593 - 600
Copyright
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
2. Kennedy, P. B., A property of bounded tegular functions, Proc. Roy. Irish Acad., 60, sec. A, no. 2 (1959).Google Scholar
3. Littlewood, J. E., Lectures on the Theory of Functions (Oxford, 1944).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