Mathematics > Classical Analysis and ODEs
[Submitted on 28 Jun 2024
(v1)
, last revised 28 Aug 2024 (this version, v2)]
Title: Analog version of Hausdorff--Young's theorem for quadratic Fourier transforms and boundedness of oscillatory integral operator
Title: Hausdorff–Young定理的类比版本针对二次Fourier变换和振荡积分算子的有界性
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.
Submission history
From: Tuan Trinh [view email][v1] Fri, 28 Jun 2024 19:04:09 UTC (11 KB)
[v2] Wed, 28 Aug 2024 16:14:36 UTC (10 KB)
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