Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T14:58:11.660Z Has data issue: false hasContentIssue false
  • English
  • Français

The characterization of orders for regular functions

Published online by Cambridge University Press:  24 October 2008

C. N. Linden
C. N. Linden
Affiliation:
Department of Mathematics and Computer Science, University College of Swansea, Singleton Park, Swansea SA2 SPP, Wales
Get access Rights & Permissions [Opens in a new window]

Extract

For a given function f, regular in the unit disk D(0, 1), logarithmic means of order p may be defined in terms of integrals by the formulae

for 0 < p < , and by

when 0 < r < 1. Associated p-orders are subsequently defined by

for 0 < p.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 2 , March 1992 , pp. 299 - 307
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Gardiner, S. J.. Growth properties of pth means of potentials in the unit ball. Proc. Amer. Math. Soc. 103 (1988), 861869.Google Scholar
2Linden, C. N.. The representation of regular functions. J. London Math. Soc. 39 (1964), 1930.CrossRefGoogle Scholar
3Linden, C. X.. Integral logarithmic means for regular functions. Pacific J. Math. 138 (1989), 119127.CrossRefGoogle Scholar
4Littlewood, J. E.. Theory of Functions (Oxford University Press, 1944).Google Scholar
5Tsuji, M.. Potential Theory (Maruzen, 1959).Google Scholar