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Unbounded subharmonic functions bounded in one tract

Published online by Cambridge University Press:  24 October 2008

G. A. CÁmera
G. A. CÁmera
Affiliation:
Dpto. de Matemáticas, Facultad de Ciencias, U.C.V., Caracas, Venezuela
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Extract

In this paper we shall consider the class Hm of subharmonic functions u, unbounded in, which have a thick tract where u is bounded. We recall here that non-constant subharmonic functions in space (i.e. m ≥ 3) are not necessarily unbounded as in the two-dimensional case. For basic concepts in this area we refer the reader to [3].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 2 , September 1985 , pp. 327 - 341
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Cámera, G. A.Minimum growth rate of subharmonic functions. Acta Cient. Venezolana 30 (1979), 349–359.Google Scholar
[2]Cámera, G. A.Subharmonic functions on sets of finite measure. Quart. J. Math. Oxford (2) 33 (1982), 27–43.CrossRefGoogle Scholar
[3]Hayman, W. K. and Kennedy, P. B.Subharmonic Functions, vol. i (Academic Press, 1976).Google Scholar
[4]Landkof, N. S.Foundations of Modern Potential Theory (Springer-Verlag, 1972).CrossRefGoogle Scholar
[5]Talpur, M. N. M.On the existence of asymptotic paths for subharmonic functions in ℝ m. Proc. London Math. Soc. (3) 32 (1976), 181–192.CrossRefGoogle Scholar