Título inglés | Restriction and decay for flat hypersurfaces. |
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Título español | Restricción y decaimiento para hipersuperficies planas. |
Autor/es | Carbery, Anthony ; Ziesler, Sarah |
Organización | Dep. Math. Statist. Univ. Edinburgh, Edimburgo, Reino Unido;Dep. Math. Comput. Sci. Dominican Univ., River Forest (Illinois), Estados Unidos |
Revista | 0214-1493 |
Publicación | 2002, 46 (2): 405-434, 28 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | 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. |
Clasificación UNESCO | 120213 |
Palabras clave español | Hipersuperficies ; Curvatura ; Transformada de Fourier ; Restricción |
Código MathReviews | MR1934361 |
Acceso al artículo completo |