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A representation of distributions supported on smooth hypersurfaces of Rn

Published online by Cambridge University Press:  24 October 2008

Kanghui Guo
Kanghui Guo
Affiliation:
Department of Mathematics, Southivest Missouri State University, Springfield, Missouri, 65804
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Extract

Let S(Rn) be the space of Schwartz class functions. The dual space of S′(Rn), S(Rn), is called the temperate distributions. In this article, we call them distributions. For 1 ≤ p ≤ ∞, let FLp(Rn) = {f:∈ Lp(Rn)}, then we know that FLp(Rn) ⊂ S′(Rn), for 1 ≤ p ≤ ∞. Let U be open and bounded in Rn−1 and let M = {(x, ψ(x));x ∈ U} be a smooth hypersurface of Rn with non-zero Gaussian curvature. It is easy to see that any bounded measure σ on Rn−1 supported in U yields a distribution T in Rn, supported in M, given by the formula

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 1 , January 1995 , pp. 153 - 160
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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