Linear adjoint restriction estimates for paraboloid

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 Schrödinger equation under the assumption that the initial datum has additional angular regularity.

24 pages

References in corpus (2)

• Strichartz estimates for wave equation with inverse square potential
• Radial multipliers and restriction to surfaces of the Fourier transform in mixed-norm spaces

Cited by in corpus (2)

• Linear restriction estimates for Schroedinger equation on metric cones
• Radial multipliers and restriction to surfaces of the Fourier transform in mixed-norm spaces