Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-11T04:20:13.074Z Has data issue: false hasContentIssue false
  • English
  • Français

The hardy class of functions of bounded argument rotation

Published online by Cambridge University Press:  09 April 2009

Sanford S. Miller  and
Petru T. Mocanu
Sanford S. Miller
Affiliation:
State University of New York, Brockport, N. Y. 14420, U.S.A.
Petru T. Mocanu
Affiliation:
The Babes-Bolyai University, Cluj Romania.
Rights & Permissions [Opens in a new window]

Abstract

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.

The Hardy classes for functions of bounded argument rotation and their derivatives are determined. In addition, if , then growth conditions for an are obtained.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1976 , pp. 72 - 78
Copyright
Copyright © Australian Mathematical Society 1976

References

Biernacki, M. (1947–1948), ‘Sur une inégalité entre les moyennes des dérivées logarithmiques’, Mathematica (Cluj) 23, 54–59.Google Scholar
Brennan, D. A. (1968–1969), ‘On functions of bounded boundary rotation I’, Proc. Edinburgh Math. Soc. 16, 334–347.Google Scholar
Eenigenburg, P. J. and Keogh, F. R. (1970), ‘On the Hardy class of some univalent functions and their derivatives’, Michigan Math. J. 17, 335–346.CrossRefGoogle Scholar
Hardy, G. H. and Littlewood, J. E. (1932), ‘Some properties of fractional integrals. II’, Math. Z. 34, 403–439.CrossRefGoogle Scholar
Löwner, K. (1917), Untersuchungen über die Verzerrung bei konformen Abbildungen des Einheitskreises ¦z¦ < 1, die Funktionen mit nicht verschwindender Ableitung geliefert werden (Ber. der Kön. Sächsischen Gesellschaft der Wiss., Zu Leipzig, 1917), 26.Google Scholar
Lohwater, A. J., Piranian, E. and Rudin, W. (1955), ‘The derivative of a Schlicht function’. Math. Scand. 3, 103–106.CrossRefGoogle Scholar
Noonan, J. (1972), ‘On functions of bounded rotation’, Proc. Amer. Math. Soc. 32, 91–101.CrossRefGoogle Scholar
Paatero, V. (1931), Über die konformen Abbildungen von Gebieten deren Ränder von beschränkter Drehung sind’, Ann. Acad. Sci. Penn. Ser. A I 33, No. 9.Google Scholar
Pinchuk, B. (1973), ‘The Harfy clas of functions of bounded boundary rotation’, Proc. Amer. Math. Soc. 38, 355–360.CrossRefGoogle Scholar
Tammi, O. (1952), ‘On the maximalization of the coefficients of Schlicht and related function’, Ann. Acad. Sci. Fenn. Ser. A I 114.Google Scholar