We study the action of Fourier Integral Operators (FIOs) of Hoermander's type on F L^p, $1\leq p\leq\infty$. We see, from the Beurling-Helson theorem, that generally FIOs of order zero fail to be bounded on these spaces when $p\not=2$, the counterexample being given by any smooth non-linear change of variable. Here we show that FIOs of order $m=-d|1/2-1/p|$ are instead bounded. Moreover, this loss of derivatives is proved to be sharp in every dimension $d\geq1$, even for phases which are linear in the dual variables. The proofs make use of tools from time-frequency analysis such as the theory of modulation spaces.

### Boundedness of Fourier Integral Operators on F L^p spaces

#### Abstract

We study the action of Fourier Integral Operators (FIOs) of Hoermander's type on F L^p, $1\leq p\leq\infty$. We see, from the Beurling-Helson theorem, that generally FIOs of order zero fail to be bounded on these spaces when $p\not=2$, the counterexample being given by any smooth non-linear change of variable. Here we show that FIOs of order $m=-d|1/2-1/p|$ are instead bounded. Moreover, this loss of derivatives is proved to be sharp in every dimension $d\geq1$, even for phases which are linear in the dual variables. The proofs make use of tools from time-frequency analysis such as the theory of modulation spaces.
##### Scheda breve Scheda completa Scheda completa (DC)
361
11
6049
6071
http://arxiv.org/pdf/0801.1444v3.pdf
Beurling-Helson's theorem; FL^p spaces; Fourier Integral Operators; Modulation spaces; Short-time Fourier transform
E. Cordero; F. Nicola; L. Rodino
File in questo prodotto:
File
FIOtransAMS.pdf

Accesso riservato

Tipo di file: POSTPRINT (VERSIONE FINALE DELL’AUTORE)
Dimensione 335.39 kB
Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/44264