Linear adjoint restriction estimates for paraboloid
Analysis of PDEs
2019-06-12 v2
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.
Keywords
Cite
@article{arxiv.1507.06100,
title = {Linear adjoint restriction estimates for paraboloid},
author = {Changxing Miao and Junyong Zhang and Jiqiang Zheng},
journal= {arXiv preprint arXiv:1507.06100},
year = {2019}
}
Comments
24 pages