Analog version of Hausdorff--Young's theorem for quadratic Fourier transforms and boundedness of oscillatory integral operator

Abstract: The purpose of this paper is twofold. The first aim is based on Riesz--Thorin's interpolation theorem, we prove new Hausdorff--Young type inequalities for the Quadratic Fourier transforms in (Ann. Funct. Anal. 2014;5(1):10--23) and linear canonical transforms in (Mediterr. J. Math. 2018;15,13), which were introduced by Castro et al. The second aim is to investigate the boundedness of the oscillatory integral operator with polynomial phases, which is also presented in the last section of the article.