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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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References

[1] Domar, Y.. On the spectral synthesis problem for (n − 1)-dimensional subsets of ℝn, n≥2. Ark. Mat. 9 (1971), 23–37.CrossRefGoogle Scholar
[2] Drury, S. W. and Marshall, B. P.. Fourier restriction theorems for curves with affine and Euclidean arc lengths. Math. Proc. Cambridge Philos. Soc. 97 (1985), 111–125.CrossRefGoogle Scholar
[3] Hörmander, L.. Oscillatory integrals and multipliers on FLp. Ark. Mat. 11 (1973), 1–11.CrossRefGoogle Scholar
[4] Hörmander, L.. Lower bounds at infinity for solutions of differential equations with constant coefficients. Israel J. Math. 16 (1973), 103–116.CrossRefGoogle Scholar
[5] Littman, W.. Fourier transforms of surface-carried measures and differentiability of surface averages. Bull. Amer. Math. Soc. 69 (1963), 766–770.CrossRefGoogle Scholar
[6] Pollard, H.. The harmonic analysis of bounded functions. Duke Math. J. 20 (1953), 499–512.CrossRefGoogle Scholar
[7] Stein, E. M.. Singular Integrals and Differentiability Properties of Functions (Princeton University Press, 1970).Google Scholar
[8] Stein, E. M. and Wainger, S.. Problems in harmonic analysis related to curvature. Bull. Amer. Math. Soc. 84 (1978), 1239–1295.CrossRefGoogle Scholar