In the first part we consider restriction theorems for hypersurfaces Γ in R n , with the affine curvature K 1/(n+1) Γ 2000 Mathematics Subject Classification. 42B99.
We obtain V estimates for singular integrals and maximal functions associated to hypersurfaces F in R n+1 , n ^ 2, which are obtained by rotating a curve around one of the coordinate axes.
We prove an optimal restriction theorem for an arbitrary homogeneous polynomial hypersurface (of degree at least 2) in R 3 , with affine curvature introduced as a mitigating factor.
Abstract. We investigate restriction theorems for hypersurfaces of revolution in R 3 , with affine curvature introduced as a mitigating factor. Abi-Khuzam and Shayya recently showed that a Stein-Tomas restriction theorem can be obtained for a class of convex hypersurfaces that includes the surfaces Γ(x) = (x, e −1/|x| m ), m ≥ 1. We enlarge their class of hypersurfaces and give a much simplified proof of their result.
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