Analysis & PDE

  • Anal. PDE
  • Volume 12, Number 4 (2019), 1115-1148.

Optimal multilinear restriction estimates for a class of hypersurfaces with curvature

Ioan Bejenaru

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Abstract

Bennett, Carbery and Tao (2006) considered the k -linear restriction estimate in n + 1 and established the near optimal L 2 ( k 1 ) estimate under transversality assumptions only. In 2017, we showed that the trilinear restriction estimate improves its range of exponents under some curvature assumptions. In this paper we establish almost sharp multilinear estimates for a class of hypersurfaces with curvature for 4 k n . Together with previous results in the literature, this shows that curvature improves the range of exponents in the multilinear restriction estimate at all levels of lower multilinearity, that is, when k n .

Article information

Source
Anal. PDE, Volume 12, Number 4 (2019), 1115-1148.

Dates
Received: 28 February 2018
Revised: 25 May 2018
Accepted: 29 June 2018
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.apde/1540864863

Digital Object Identifier
doi:10.2140/apde.2019.12.1115

Mathematical Reviews number (MathSciNet)
MR3869388

Zentralblatt MATH identifier
06991229

Subjects
Primary: 42B15: Multipliers
Secondary: 42B25: Maximal functions, Littlewood-Paley theory

Keywords
multilinear restriction estimates shape operator wave packets

Citation

Bejenaru, Ioan. Optimal multilinear restriction estimates for a class of hypersurfaces with curvature. Anal. PDE 12 (2019), no. 4, 1115--1148. doi:10.2140/apde.2019.12.1115. https://projecteuclid.org/euclid.apde/1540864863


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