# Restriction and decay for flat hypersurfaces.

Anthony Carbery; Sarah Ziesler

Publicacions Matemàtiques (2002)

- Volume: 46, Issue: 2, page 405-434
- ISSN: 0214-1493

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topCarbery, 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 -

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