The Fourier extension operator on large spheres and related oscillatory integrals

Abstract

We obtain new estimates for a class of oscillatory integral operators with folding canonical relations satisfying a curvature condition. The main lower bounds showing sharpness are proved using Kakeya set constructions. As a special case of the upper bounds we deduce optimal Lp(𝕤2)→Lq(R𝕤2) estimates for the Fourier extension operator on large spheres in ℝ3, which are uniform in the radius R. Two appendices are included, one concerning an application to Lorentz space bounds for averaging operators along curves in ℝ3, and one on bilinear estimates.

Locations

• Proceedings of the London Mathematical Society - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View