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arXiv · 1507.06100

Linear adjoint restriction estimates for paraboloid

Changxing Miao·Junyong Zhang·Jiqiang Zheng
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Abstract

We prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes the paraboloid restriction estimate in radial case from [Shao, Rev. Mat. Iberoam. 25(2009), 1127-1168], as well as the result from [Miao et al. Proc. AMS 140(2012), 2091-2102]. As an application, we show a local smoothing estimate for a solution of the linear Schr\"odinger equation under the assumption that the initial datum has additional angular regularity.

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Changxing Miao, Junyong Zhang, Jiqiang Zheng. 2015-07-22. Linear adjoint restriction estimates for paraboloid. https://arxiv.org/abs/1507.06100

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