Vol. 10, No. 8, 2017

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
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 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 L2 × L2 Lq 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
Received: 23 January 2017
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