Restriction and decay for flat hypersurfaces.

Carbery, Anthony, and Ziesler, Sarah. "Restriction and decay for flat hypersurfaces.." Publicacions Matemàtiques 46.2 (2002): 405-434. <http://eudml.org/doc/41458>.

@article{Carbery2002,
abstract = {In the first part we consider restriction theorems for hypersurfaces Γ in Rn, with the affine curvature KΓ1/(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 second part we discuss decay estimates for the Fourier transform of the density KΓ1/2 supported on the surface and investigate the relationship between restriction and decay in this setting. It is well-known that restriction theorems follow from appropriate decay estimates; one would like to know whether restriction and decay are, in fact, equivalent. We show that this is not the case in two dimensions. We also go some way towards a classification of those curves/surfaces for which decay holds by giving some sufficient conditions and some necessary conditions for decay.},
author = {Carbery, Anthony, Ziesler, Sarah},
journal = {Publicacions Matemàtiques},
keywords = {Hipersuperficies; Curvatura; Transformada de Fourier; Restricción; Fourier transform; restriction theorems; decay estimates},
language = {eng},
number = {2},
pages = {405-434},
title = {Restriction and decay for flat hypersurfaces.},
url = {http://eudml.org/doc/41458},
volume = {46},
year = {2002},
}

TY - JOUR
AU - Carbery, Anthony
AU - Ziesler, Sarah
TI - Restriction and decay for flat hypersurfaces.
JO - Publicacions Matemàtiques
PY - 2002
VL - 46
IS - 2
SP - 405
EP - 434
AB - In the first part we consider restriction theorems for hypersurfaces Γ in Rn, with the affine curvature KΓ1/(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 second part we discuss decay estimates for the Fourier transform of the density KΓ1/2 supported on the surface and investigate the relationship between restriction and decay in this setting. It is well-known that restriction theorems follow from appropriate decay estimates; one would like to know whether restriction and decay are, in fact, equivalent. We show that this is not the case in two dimensions. We also go some way towards a classification of those curves/surfaces for which decay holds by giving some sufficient conditions and some necessary conditions for decay.
LA - eng
KW - Hipersuperficies; Curvatura; Transformada de Fourier; Restricción; Fourier transform; restriction theorems; decay estimates
UR - http://eudml.org/doc/41458
ER -