Optimal multilinear restriction estimates for a class of hypersurfaces with curvature

Bejenaru, Ioan

doi:10.2140/apde.2019.12.1115

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Optimal multilinear restriction estimates for a class of hypersurfaces with curvature

Ioan Bejenaru

Vol. 12 (2019), No. 4, 1115–1148

DOI: 10.2140/apde.2019.12.1115

Abstract

Bennett, Carbery and Tao (2006) considered the $k$ -linear restriction estimate in $ℝ^{n + 1}$ 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 $4 \leq k \leq n$ . 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 $k \leq n$ .

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Keywords

multilinear restriction estimates, shape operator, wave packets

Mathematical Subject Classification 2010

Primary: 42B15

Secondary: 42B25

Milestones

Received: 28 February 2018

Revised: 25 May 2018

Accepted: 29 June 2018

Published: 20 October 2018

Authors

Ioan Bejenaru
Department of Mathematics University of California, San Diego La Jolla, CA United States

Vol. 12, No. 4, 2019