The multilinear restriction estimate: a short proof and a refinement

We provide an alternative and self contained proof of the main result of Bennett, Carbery, and Tao regarding the multilinear restriction estimate. The approach is inspired by the recent result of Guth about the Kakeya version of multilinear restriction estimate. At lower levels of multilinearity we provide a refined estimate in the context of small support for one of the terms involved.

Keywords

multilinear restriction estimates, induction on scale

2010 Mathematics Subject Classification

Primary 42B15. Secondary 42B25.

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Part of this work was supported by a grant from the Simons Foundation (#359929, Ioan Bejenaru). Part of this work was supported by the National Science Foundation under grant No. DMS-1440140 while the author was in residence at the Mathematical Research Sciences Institute in Berkeley, California, during the Fall 2015 semester. Part of this work was supported by an NSF grant, DMS-1600444.

Received 15 March 2016

Accepted 18 July 2016

Published 29 January 2018