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Boundary behaviour of harmonic functions and solutions of parabolic systems

Published online by Cambridge University Press:  20 January 2009

N. A. Watson
N. A. Watson
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand
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In [1], Calderón proved that, if u is a harmonic function on Rn × ]0, ∞[, and at each point ξ of a subset E of Rn, u is bounded in some cone with vertex (ξ, 0), then u has a nontangential limit at almost every point of E × {0}. The main result of this note is a stronger version of this theorem, in which the hypotheses remain unchanged but the nontangential limits in the conclusion are replaced by limits through the more general approach regions first considered by Nagel and Stein in [7].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 2 , June 1988 , pp. 267 - 270
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

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