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
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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