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2019 Optimal multilinear restriction estimates for a class of hypersurfaces with curvature
Ioan Bejenaru
Anal. PDE 12(4): 1115-1148 (2019). DOI: 10.2140/apde.2019.12.1115

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 .

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Ioan Bejenaru. "Optimal multilinear restriction estimates for a class of hypersurfaces with curvature." Anal. PDE 12 (4) 1115 - 1148, 2019. https://doi.org/10.2140/apde.2019.12.1115

Information

Received: 28 February 2018; Revised: 25 May 2018; Accepted: 29 June 2018; Published: 2019
First available in Project Euclid: 30 October 2018

zbMATH: 06991229
MathSciNet: MR3869388
Digital Object Identifier: 10.2140/apde.2019.12.1115

Subjects:
Primary: 42B15
Secondary: 42B25

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 4 • 2019
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