Vol. 12, No. 4, 2019

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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

Bennett, Carbery and Tao (2006) considered the k-linear restriction estimate in n+1 and established the near optimal L2(k1) 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.

multilinear restriction estimates, shape operator, wave packets
Mathematical Subject Classification 2010
Primary: 42B15
Secondary: 42B25
Received: 28 February 2018
Revised: 25 May 2018
Accepted: 29 June 2018
Published: 20 October 2018
Ioan Bejenaru
Department of Mathematics
University of California, San Diego
La Jolla, CA
United States