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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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

multilinear restriction estimates shape operator wave packets


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.

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