Hörmander oscillatory integral operators:A revisit  

作　　者：Chuanwei Gao Zhong Gao Changxing Miao 

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China [2]Institute of Applied Physics and Computational Mathematics,Beijing 100088,China

出　　处：《Science China Mathematics》2025年第4期873-890,共18页中国科学(数学英文版)

基　　金：supported by the National Key R&D Program of China(Grant No.2022YFA1005700);supported by National Natural Science Foundation of China(Grant No.12301121);supported by National Natural Science Foundation of China(Grant No.12371095)。

摘　　要：In this paper,we present new proofs for both the sharp Lp estimate and the decoupling theorem for the Hörmander oscillatory integral operator.The sharp Lp estimate was previously obtained by Stein(1986)and Bourgain and Guth(2011)via the TT^(*) and multilinear methods,respectively.We provide a unified proof based on the bilinear method for both odd and even dimensions.The strategy is inspired by Barron’s work(2022)on the restriction problem.The decoupling theorem for the Hörmander oscillatory integral operator can be obtained by the approach in Beltran et al.(2020),where the key observation can be roughly formulated as follows:in a physical space of sufficiently small scale,the variable setting can be essentially viewed as translation-invariant.In contrast,we reprove the decoupling theorem for the Hörmander oscillatory integral operator through the Pramanik-Seeger approximation approach(Pramanik and Seeger(2007)).Both proofs rely on a scale-dependent induction argument,which can be used to deal with perturbation terms in the phase function.

关 键 词：Hormander oscillatory integral operators bilinear method decoupling inequality induction argument Broad-Narrow analysis 

分 类 号：O177.6[理学—数学]