#### Vol. 10, No. 8, 2017

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Bilinear restriction estimates for surfaces of codimension bigger than 1

### Jong-Guk Bak, Jungjin Lee and Sanghyuk Lee

Vol. 10 (2017), No. 8, 1961–1985
##### Abstract

In connection with the restriction problem in ${ℝ}^{n}$ for hypersurfaces including the sphere and paraboloid, the bilinear (adjoint) restriction estimates have been extensively studied. However, not much is known about such estimates for surfaces with codimension (and dimension) larger than 1. In this paper we show sharp bilinear ${L}^{2}×{L}^{2}\to {L}^{q}$ restriction estimates for general surfaces of higher codimension. In some special cases, we can apply these results to obtain the corresponding linear estimates.

##### Keywords
Fourier transform of measures, complex surfaces, Fourier restriction estimates
##### Mathematical Subject Classification 2010
Primary: 42B15, 42B20
##### Milestones
Revised: 2 June 2017
Accepted: 12 July 2017
Published: 18 August 2017
##### Authors
 Jong-Guk Bak Department of Mathematics Pohang University of Science and Technology Pohang % 37673 South Korea Jungjin Lee Department of Mathematical Sciences School of Natural Science Ulsan National Institute of Science and Technology Ulsan % 44919 South Korea Sanghyuk Lee Department of Mathematical Sciences Seoul National University Seoul % 151-747 South Korea