Tohoku Mathematical Journal
2021
March
SECOND SERIES VOL. 73, NO. 1

Tohoku Math. J.
73 (2021), 105-118

Title REPRESENTATION OF HIGHER-ORDER DISPERSIVE OPERATORS VIA SHORT-TIME FOURIER TRANSFORM AND ITS APPLICATION

Author Keiichi Kato, Masaharu Kobayashi, Shingo Ito and Tadashi Takahashi

(Received March 8, 2017, revised December 19, 2019)
Abstract. In this paper, we propose a new representation of the solution to higher-order dispersive equations (which include the free Schrödinger equation and the Airy equation) by using the short-time Fourier transform. As its application, we give $M^{p,q}$-$M^{p,q}_s$, $M^{p,q}$-$M^{p^\prime,q}$ and Strichartz type estimates for the solutions in the framework of the modulation spaces $M^{p,q}_s$.

Mathematics Subject Classification. Primary 35C15; Secondary 42B35.
Key words and phrases. Higher-order dispersive equations, short-time Fourier transform, modulation space.

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