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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((2))> Lq(R2) estimates for the Fourier extension operator on large spheres in (3), 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 (3), and one on bilinear estimates.
Original language  English 

Pages (fromto)  4582 
Number of pages  38 
Journal  London Mathematical Society. Proceedings 
Volume  98 
Issue number  1 
Early online date  13 Jun 2008 
DOIs  
Publication status  Published  1 Jan 2009 
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Dive into the research topics of 'The Fourier extension operator on large spheres and related oscillatory integrals'. Together they form a unique fingerprint.Projects
 1 Finished

New Approaches to Central Problems in Euclidean Harmonic Analysis and Geometric Combinatorics
Engineering & Physical Science Research Council
3/01/07 → 2/01/10
Project: Research Councils