Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Strichartz type estimates for solutions to the Schrödinger equation
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by Jie Chen;
Proc. Amer. Math. Soc. 152 (2024), 3941-3953
DOI: https://doi.org/10.1090/proc/16887
Published electronically: July 17, 2024

Abstract:

In this article, we show the necessary and sufficient conditions for the inequality \begin{equation*} \|u\|_{L_t^qL_x^r}\lesssim \|u\|_{X^{s,b}}, \end{equation*} where $\|u\|_{X^{s,b}}≔\|\hat {u}(\tau ,\xi )\langle \xi \rangle ^s\langle \tau +|\xi |^2\rangle ^b \|_{L_{\tau ,\xi }^2}$. These estimates are also referred to as Strichartz estimates related to Schrödinger equation. We also give a new proof of the maximal function estimates for solutions to Schrödinger and Airy equations.
References
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Bibliographic Information
  • Jie Chen
  • Affiliation: School of Science, Jimei University, Xiamen 361021, People’s Republic of China
  • ORCID: 0000-0003-3457-6334
  • Received by editor(s): December 3, 2023
  • Received by editor(s) in revised form: March 30, 2024
  • Published electronically: July 17, 2024
  • Additional Notes: The author was supported by the NSFC, grants 12301116.
  • Communicated by: Benoit Pausader
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3941-3953
  • MSC (2020): Primary 35Q55
  • DOI: https://doi.org/10.1090/proc/16887
  • MathSciNet review: 4781986