. A P ] 4 S ep 2 00 6 OPTIMAL REGULARITY OF FOURIER INTEGRAL OPERATORS WITH ONE - SIDED FOLDS

. A P ] 1 S ep 2 00 6 OPTIMAL REGULARITY OF FOURIER INTEGRAL OPERATORS WITH ONE - SIDED FOLDS

We obtain optimal continuity in Sobolev spaces for the Fourier integral operators associated to singular canonical relations, when one of the two projections is a Whitney fold. The regularity depends on the type, k, of the other projection from the canonical relation (k = 1 for a Whitney fold). We prove that one loses (4 + 2 k) −1 of a derivative in the regularity properties. The proof is based...

Optimal Regularity Of Fourier Integral Operators With One-Sided Folds

A Calderón–zygmund Estimate with Applications to Generalized Radon Transforms and Fourier Integral Operators

We prove a Calderón–Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators, generalized Radon transforms and singular oscillatory integrals. The main theme in this paper is to strengthen various sharp L–Sobolev regularity results for integral operators. To illustrate this we consider the example of spherical means. Let σ den...

. 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...

ar X iv : m at h / 06 09 02 4 v 1 [ m at h . A P ] 1 S ep 2 00 6 L p - L q regularity of Fourier integral operators with caustics

The caustics of Fourier integral operators are defined as caustics of the corresponding Schwartz kernels (Lagrangian distributions on X × Y). The caustic set Σ(C) of the canonical relation C is characterized as the set of points where the rank of the projection π : C → X × Y is smaller than its maximal value, dim(X × Y) − 1. We derive the L p (Y) → L q (X) estimates on Fourier integral operator...