Methods and Applications of Analysis

Volume 28 (2021)

Number 4

Special issue dedicated to Professor Ling Hsiao on the occasion of her 80th birthday, Part III

Guest editors: Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing), Hailiang Li (Capital Normal University, Beijing), Tao Luo (City University of Hong Kong), and Zhouping Xin (Chinese University of Hong Kong)

Oscillatory integrals involving the Carleson–Sjölin conditions and several applications

Pages: 467 – 486

DOI: https://dx.doi.org/10.4310/MAA.2021.v28.n4.a4

Authors

Changxing Miao (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Jianwei-Urbain Yang (Department of Mathematics, Beijing Institute of Technology, Beijing, China)

Abstract

This short exposition is devoted to a brief overview of several challenging problems in modern harmonic analysis. Some of them have been through a considerably long period of time while the others are developed very recently. The clue that we intend to follow is the development of the restriction theorem in harmonic analysis and the theory of oscillatory integrals satisfying the Carleson–Sjölin conditions. We try to summarize all the recent results on these related problems.

Keywords

Fourier integral operators, Kakeya and restriction conjecture, local smoothing, Carleson–Sjölin conditions, oscillatory integral

2010 Mathematics Subject Classification

42B20, 42B25

Full Text (PDF format)

This work is supported in part by the National Natural Science Foundation of China under grant No.12026407 (Tianyuan project). The second author is also supported by NSFC grant No. 11901032 and Research fund program for young scholars of Beijing Institute of Technology.

Received 16 September 2020

Accepted 17 December 2020

Published 10 June 2022