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Restriction implies Bochner–Riesz for paraboloids

Published online by Cambridge University Press:  24 October 2008

Anthony Carbery
Anthony Carbery
Affiliation:
Mathematics Division, University of Sussex, Falmer, Brighton BNl 9QH
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Extract

Let Σ ⊆ ℝn be a (compact) hypersurface with non-vanishing Gaussian curvature, with suitable parameterizations, also called Σ: U → ℝn (U open patches in ℝn−1). The restriction problem for Σ is the question of the a priori estimate (for f ∈ S(ℝ))

(^denoting the Fourier transform). The Bochner-Riesz problem for Σ is the question of whether the functions

define Lp-bounded Fourier multiplier operators on ℝn in the range

.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 3 , May 1992 , pp. 525 - 529
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

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