Analysis & PDE
- Anal. PDE
- Volume 12, Number 4 (2019), 1115-1148.
Optimal multilinear restriction estimates for a class of hypersurfaces with curvature
Bennett, Carbery and Tao (2006) considered the -linear restriction estimate in and established the near optimal 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 . 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 .
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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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