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arXiv · 1707.08944

Multi-scale bilinear restriction estimates for general phases

Timothy Candy
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Abstract

We prove (adjoint) bilinear restriction estimates for general phases at different scales in the full non-endpoint mixed norm range, and give bounds with a sharp and explicit dependence on the phases. These estimates have applications to high-low frequency interactions for solutions to partial differential equations, as well as to the linear restriction problem for surfaces with degenerate curvature. As a consequence, we obtain new bilinear restriction estimates for elliptic phases and wave/Klein-Gordon interactions in the full bilinear range, and give a refined Strichartz inequality for the Klein-Gordon equation. In addition, we extend these bilinear estimates to hold in adapted function spaces by using a transference type principle which holds for vector valued waves.

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Timothy Candy. 2017-07-27. Multi-scale bilinear restriction estimates for general phases. https://arxiv.org/abs/1707.08944

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