Strichartz type estimates for solutions to the Schrödinger equation

Chen, Jie

doi:10.1090/proc/16887

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.

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Strichartz type estimates for solutions to the Schrödinger equation
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Abstract: