Oscillatory and Fourier Integral Operators with Degenerate Canonical Relations
نویسندگان
چکیده
In (1.1) it is assumed that the real-valued phase function Φ is smooth in ΩL × ΩR where ΩL,ΩR are open subsets of R d and amplitude σ ∈ C 0 (ΩL × ΩR). (The assumption that dim(ΩL) = dim(ΩR) is only for convenience; many of the definitions, techniques and results described below have some analogues in the nonequidimensional setting.) The L boundedness properties of Tλ are determined by the geometry of the canonical relation
منابع مشابه
Integral Operators with Singular Canonical Relations
We derive certain estimates and asymptotics for oscillatory integral operators with degenerate phase functions, concentrating our attention on the situation when one of the projections from the associated canonical relation is a Whitney fold. We discuss related topics: convexity, higher order degeneracy of canonical relations, and almost orthogonality. In the second part of the paper, we apply ...
متن کامل. A P ] 4 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 ) of a derivative in the regularity properties. The proof is based on...
متن کامل. 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...
متن کاملThe 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...
متن کامل