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arXiv · 1602.06936

Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces

Changxing Miao·Christopher D. Sogge·Yakun Xi·Jianwei Yang
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Abstract

We obtain an improvement of the bilinear estimates of Burq, G\'erard and Tzvetkov in the spirit of the refined Kakeya-Nikodym estimates of Blair and the second author. We do this by using microlocal techniques and a bilinear version of H\"ormander's oscillatory integral theorem.

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Changxing Miao, Christopher D. Sogge, Yakun Xi, Jianwei Yang. 2016-02-22. Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces. https://doi.org/10.1016/j.jfa.2016.04.015

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