Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-28T07:10:38.084Z Has data issue: false hasContentIssue false
  • English
  • Français

A weighted hyperplane mean associated with harmonic majorization in half-spaces

Published online by Cambridge University Press:  20 January 2009

D. H. Armitage
D. H. Armitage
Affiliation:
The Queen's University, Belfast BT7 1NN
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.

The purpose of this paper is to introduce a new kind of weighted hyperplane mean for subharmonic functions and to use this mean in giving results on the harmonic majorization of subharmonic functions of restricted growth in half-spaces.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 1 , February 1986 , pp. 75 - 91
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

REFERENCES

1.Armitage, D. H., On hyperplane mean values of subharmonic functions, J. London Math. Soc. (2) 22 (1980), 99–109.CrossRefGoogle Scholar
2.Brawn, F. T., The Green and Poisson kernels for the strip Rnx]0, l[, J. London Math. Soc. (2) 2 (1970), 439–454.CrossRefGoogle Scholar
3.Brawn, F. T., The Poisson integral and harmonic majorization in Rn x ]0,1[, J. London Math. Soc. (2) 3 (1971), 747–760.CrossRefGoogle Scholar
4.Brawn, F. T., Positive harmonic majorization of subharmonic functions in strips, Proc. London Math. Soc. (3) 27 (1973), 261–289.CrossRefGoogle Scholar
5.Brelot, M., Éléments de la théorie classique du potentiel (C.D.U., Paris, 1965).Google Scholar
6.Dinghas, A., Über positive harmonische Funktionen in einen Halbraum, Math. Z. 46 (1940), 559–570.CrossRefGoogle Scholar
7.Flett, T. M., On the rate of growth of mean values of holomorphic and harmonic functions, Proc. London Math. Soc. (3) 20 (1970), 749–768.CrossRefGoogle Scholar
8.Helms, L. L., Introduction to Potential Theory (Wiley-Interscience, New York, 1969).Google Scholar
9.Kuran, Ü., Harmonic majorization in half–balls and half-spaces, Proc. London Math. Soc. (3) 21 (1970), 614–636.CrossRefGoogle Scholar
10.Kuran, Ü., On the half-spherical means of subharmonic functions in half-spaces, J. London Math. Soc. (2) 2 (1970), 305–317.CrossRefGoogle Scholar
11.Kuran, Ü., A criterion of harmonic majorization in half-spaces, Bull. London Math. Soc. 3 (1971), 21–22.CrossRefGoogle Scholar
12.Nualtaranee, S., On least harmonic majorants in half-spaces, Proc. London Math. Soc. (3) 22 (1973), 243–260.CrossRefGoogle Scholar
13.Tsuji, M., Potential Theory in Modern Function Theory (Maruzen, Tokyo, 1959).Google Scholar
14.Watson, G. N., A Treatise on the Theory of Bessel Functions (C.U.P., Cambridge, 1922).Google Scholar
15.Watson, N. A., A limit function associated with harmonic majorization on half-spaces, J. London Math. Soc. (2) 9 (1974), 229–238.CrossRefGoogle Scholar