A Bilinear Oscillatory Integral along Parabolas
نویسندگان
چکیده
We establish an L×L → L norm estimate for a bilinear oscillatory integral operator along parabolas incorporating oscillatory factors e −β .
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 کاملEndpoint Estimates for Bilinear Oscillatory Integral Operators Related to Restriction to the Cone
We prove an endpoint estimate for oscillatory integral operators whose phase function satisfies the cinematic curvature condition. It is a generalization of a result due to Tao (2001).
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 کامل2 1 Se p 20 06 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 p (S 2) → L q (RS 2) estimates for the Fourier extension operator on large spheres in R 3 , which are uniform in the ra...
متن کاملBilinear Fourier Integral Operators
We study the boundedness of bilinear Fourier integral operators on products of Lebesgue spaces. These operators are obtained from the class of bilinear pseudodifferential operators of Coifman and Meyer via the introduction of an oscillatory factor containing a real-valued phase of five variables Φ(x, y1, y2, ξ1, ξ2) which is jointly homogeneous in the phase variables (ξ1, ξ2). For symbols of or...
متن کامل