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On local smoothing problems and Stein's maximal spherical means


Authors: Changxing Miao, Jianwei Yang and Jiqiang Zheng
Journal: Proc. Amer. Math. Soc. 145 (2017), 4269-4282
MSC (2010): Primary 42B25, 42B20
DOI: https://doi.org/10.1090/proc/13313
Published electronically: July 7, 2017
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Abstract: It is proved that the local smoothing conjecture for wave equations implies certain improvements on Stein's analytic family of maximal spherical means. Some related problems are also discussed.


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Changxing Miao
Affiliation: Institute of Applied Physics and Computational Mathematics, Beijing 100088, People’s Republic of China
Email: miao_changxing@aliyun.com, miao_{}changxing@iapcm.ac.cn

Jianwei Yang
Affiliation: Beijing International Center for Mathematical Research, Peking University, Beijing 100871, People’s Republic of China – and – LAGA(UMR 7539), Institut Galilée, Université Paris 13, Sorbonne Paris Cité, France
Email: geewey_{}young@pku.edu.cn

Jiqiang Zheng
Affiliation: Université de Nice - Sophia Antipolis, Laboratoire J. A. Dieudonné, 06108 Nice Cedex 02, France
Email: zhengjiqiang@gmail.com

DOI: https://doi.org/10.1090/proc/13313
Keywords: Maximal spherical means, local smoothing, wave equation, oscillatory integral
Received by editor(s): June 5, 2014
Published electronically: July 7, 2017
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2017 American Mathematical Society

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