2 1 Se p 20 06 THE FOURIER EXTENSION OPERATOR ON LARGE SPHERES AND RELATED OSCILLATORY
نویسنده
چکیده
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 L p (S 2) → L q (RS 2) estimates for the Fourier extension operator on large spheres in R 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 R 3 , and one on bilinear estimates.
منابع مشابه
The Fourier Extension Operator on Large Spheres and Related Oscillatory Integrals
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 L(S) → L(RS) estimates for the Fourier extension operator on large spheres in R, which are uniform in the radius R. Two a...
متن کامل. C A ] 4 A ug 2 00 6 THE FOURIER EXTENSION OPERATOR ON LARGE SPHERES AND RELATED OSCILLATORY
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 L(S) → L(RS) estimates for the Fourier extension operator on large spheres in R, which are uniform in the radius R. Two a...
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