Hilbert transforms and maximal functions along rough flat curves.
Restriction and decay for flat hypersurfaces.
In the first part we consider restriction theorems for hypersurfaces Γ in Rn, with the affine curvature KΓ 1/(n+1) introduced as a mitigating factor. Sjölin, [19], showed that there is a universal restriction theorem for all convex curves in R2. We show that in dimensions greater than two there is no analogous universal restriction theorem for hypersurfaces with non-negative curvature. In the...
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