English

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

R2 v1 2026-06-22T10:16:15.743Z