We study the action of Fourier Integral Operators (FIOs) of H¨ormander’s type on FL^p(R^d)_comp, 1 ≤ p≤∞. 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 ≥ 1, 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 FL^p spaces / Cordero, Elena; Nicola, Fabio; Rodino, Luigi. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 361:11(2009), pp. 6049-6071.

Boundedness of Fourier integral operators on FL^p spaces

NICOLA, FABIO;
2009

Abstract

We study the action of Fourier Integral Operators (FIOs) of H¨ormander’s type on FL^p(R^d)_comp, 1 ≤ p≤∞. 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 ≥ 1, 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.
File in questo prodotto:
File Dimensione Formato  
51338_UPLOAD.pdf

non disponibili

Tipologia: Altro materiale allegato
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 335.39 kB
Formato Adobe PDF
335.39 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1661770
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo