- boundedness of integral operators with oscillatory kernels: linear versus quadratic phases. Issue 8 (11th June 2017)

• Record Type: Journal Article
• Authors: Abdelhakim, Ahmed A.
• Is Part Of: Applicable analysis. Volume 96:Issue 8(2017)
• Page Start: 1342
• Page End: 1357
• Publication Date: 2017-06-11
• Subjects: Strichartz estimates for the Schrödinger equation -- oscillatory integrals -- – boundedness; 35B45 -- 35Q55 -- 42B20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1192135
• Languages: English
• ISSNs: 0003-6811

Abstract

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.