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On the p-approximate property for hypersurfaces of ℝn

Published online by Cambridge University Press:  04 October 2011

Kanghui Guo
Kanghui Guo
Affiliation:
Department of Mathematics, McGill University, Montreal H3A 2K6, Canada
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Extract

Let S(ℝn) be the space of Schwartz class functions and S'(ℝn) be the dual space of S(ℝn). Given a k-dimensional manifold M in ℝn with area (in case k = 1, M is a curve with length), then for 1 ≤ p ≤ ∞ we say that M has the p-approximate property of for each TεS'(ℝn) with supp T⊆M, and εLp(ℝn), we can find a sequence of measures {Tj,j = 1,2,…} on M, absolutely continuous with respect to the area measure on M, such that ∥j-∥p → 0 as j → ∞.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 503 - 511
Copyright
Copyright © Cambridge Philosophical Society 1989

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