Restriction estimates of [Formula: see text] -removal type for k-th powers and paraboloids

We obtain restriction estimates of [Formula: see text] -removal type for the set of k-th powers of integers, and for discrete d-dimensional surfaces of the form [Formula: see text] which we term ‘k-paraboloids’. For these surfaces, we obtain a satisfying range of exponents for large values of d, k....

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Detalles Bibliográficos
Autores principales: Henriot, Kevin, Hughes, Kevin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6411130/
https://www.ncbi.nlm.nih.gov/pubmed/30930489
http://dx.doi.org/10.1007/s00208-018-1650-7
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author Henriot, Kevin
Hughes, Kevin
author_facet Henriot, Kevin
Hughes, Kevin
author_sort Henriot, Kevin
collection PubMed
description We obtain restriction estimates of [Formula: see text] -removal type for the set of k-th powers of integers, and for discrete d-dimensional surfaces of the form [Formula: see text] which we term ‘k-paraboloids’. For these surfaces, we obtain a satisfying range of exponents for large values of d, k. We also obtain estimates of [Formula: see text] -removal type in the full supercritical range for k-th powers and for k-paraboloids of dimension [Formula: see text] . We rely on a variety of techniques in discrete harmonic analysis originating in Bourgain’s works on the restriction theory of the squares and the discrete parabola.
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spelling pubmed-64111302019-03-27 Restriction estimates of [Formula: see text] -removal type for k-th powers and paraboloids Henriot, Kevin Hughes, Kevin Math Ann Article We obtain restriction estimates of [Formula: see text] -removal type for the set of k-th powers of integers, and for discrete d-dimensional surfaces of the form [Formula: see text] which we term ‘k-paraboloids’. For these surfaces, we obtain a satisfying range of exponents for large values of d, k. We also obtain estimates of [Formula: see text] -removal type in the full supercritical range for k-th powers and for k-paraboloids of dimension [Formula: see text] . We rely on a variety of techniques in discrete harmonic analysis originating in Bourgain’s works on the restriction theory of the squares and the discrete parabola. Springer Berlin Heidelberg 2018-02-23 2018 /pmc/articles/PMC6411130/ /pubmed/30930489 http://dx.doi.org/10.1007/s00208-018-1650-7 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Henriot, Kevin
Hughes, Kevin
Restriction estimates of [Formula: see text] -removal type for k-th powers and paraboloids
title Restriction estimates of [Formula: see text] -removal type for k-th powers and paraboloids
title_full Restriction estimates of [Formula: see text] -removal type for k-th powers and paraboloids
title_fullStr Restriction estimates of [Formula: see text] -removal type for k-th powers and paraboloids
title_full_unstemmed Restriction estimates of [Formula: see text] -removal type for k-th powers and paraboloids
title_short Restriction estimates of [Formula: see text] -removal type for k-th powers and paraboloids
title_sort restriction estimates of [formula: see text] -removal type for k-th powers and paraboloids
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6411130/
https://www.ncbi.nlm.nih.gov/pubmed/30930489
http://dx.doi.org/10.1007/s00208-018-1650-7
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