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Fine limits of superharmonic functions

Published online by Cambridge University Press:  24 October 2008

Stephen J. Gardiner
Stephen J. Gardiner
Affiliation:
University College, Dublin, Ireland
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Extract

Let O denote the origin of ℝn (where n ≥ 2), let B(X, r) denote the open ball in ℝn of centre X and radius r, and define φn: (0, + ∞) → ℝ by φn(t) = t2-n if n ≥ 3 and φ2(t) = log (1/t). A sequence (Xk) in B(O, 1) is said to converge regularly to O if Xk → O and there is a constant k > 1 such that φn(|Xk+1|) < Kφn(|Xk|) for each k ∈ ℕ. If n ≥ 3, this is clearly equivalent to saying that there is a constant k′ ε (0, 1) such that |Xk+1| > k′|Xk| for each k (cf. [18], p. 149).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 381 - 394
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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