On Ahlfors’ “second fundamental inequality”
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- by James A. Jenkins and Kôtaro Oikawa PDF
- Proc. Amer. Math. Soc. 62 (1977), 266-270 Request permission
Abstract:
The authors have earlier given a generalization of Ahlfors’ “Second Fundamental Inequality” which reduced significantly the restrictions on the domains involved but retained the condition that certain determining functions for the domain be of bounded variation. In this paper it is shown that the condition of bounded variation can be replaced by that of finite $2/3$-variation on any closed interval and an appropriate new formal expression is given.References
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Lars Ahlfors, Untersuchungen zur Theorie der konformen Abbildung und der ganzen Funktionen, Acta Soc. Sci. Fenn. Nova Ser. 1 (1930), 1-40.
- Jacqueline Ferrand and Jacques Dufresnoy, Extension d’une inégalité de M. Ahlfors et application au problème de la dérivée angulaire, Bull. Sci. Math. (2) 69 (1945), 165–174 (French). MR 17366
- F. W. Gehring, A note on a paper by L. C. Young, Pacific J. Math. 5 (1955), 67–72. MR 68608, DOI 10.2140/pjm.1955.5.67
- James A. Jenkins and Kôtaro Oikawa, On results of Ahlfors and Hayman, Illinois J. Math. 15 (1971), 664–671. MR 296271
- S. E. Warschawski, On conformal mapping of infinite strips, Trans. Amer. Math. Soc. 51 (1942), 280–335. MR 6583, DOI 10.1090/S0002-9947-1942-0006583-6
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 266-270
- MSC: Primary 30A30
- DOI: https://doi.org/10.1090/S0002-9939-1977-0437732-2
- MathSciNet review: 0437732