- boundedness of integral operators with oscillatory kernels: linear versus quadratic phases

Abstract

Let be the oscillatory integral operators defined by where is the unit ball in and We compare the asymptotic behaviour as of the operator norms for all We prove that, except for the dimension this asymptotic behaviour depends on the linearity or quadraticity of the phase in s only. We are led to this problem by an observation on inhomogeneous Strichartz estimates for the Schrödinger equation.

Keywords:

• Strichartz estimates for the Schrödinger equation
• oscillatory integrals
• – boundedness

AMS Subject Classifications:

• 35B45
• 35Q55
• 42B20

Notes

No potential conflict of interest was reported by the authors.