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 R^{n}, with the affine curvature K_{Γ}^{1/(n+1)} introduced as a mitigating factor. Sjölin, [19], showed that there is a universal restriction theorem for all convex curves in R^{2}. 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 K _{Γ}^{1/2} 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 |