Title :

Sobolev space estimates for a class of bilinear pseudodifferential operators lacking symbolic calculus

Author(s) :

Bernicot, Frederic [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Torres, Rodolfo [Auteur]

Journal title :

Analysis & PDE

Pages :

551-571

Publisher :

Mathematical Sciences Publishers

Publication date :

2011

ISSN :

2157-5045

English keyword(s) :

Bilinear pseudodifferential operators
exotic class
transposes
Littlewood-Paley theory
Sobolev space estimates

HAL domain(s) :

Mathématiques [math]/Analyse classique [math.CA]

English abstract : [en]

The reappearance of a sometimes called exotic behavior for linear and multilinear pseudodifferential operators is investigated. The phenomenon is shown to be present in a recently introduced class of bilinear pseudodifferential ...
Show more >The reappearance of a sometimes called exotic behavior for linear and multilinear pseudodifferential operators is investigated. The phenomenon is shown to be present in a recently introduced class of bilinear pseudodifferential operators which can be seen as more general variable coefficient counterparts of the bilinear Hilbert transform and other singular bilinear multipliers operators. The unboundedness on product of Lebesgue spaces but the boundedness on spaces of smooth functions (which is the exotic behavior referred to) of such operators is obtained. In addition, by introducing a new way to approximate the product of two functions, estimates on a new paramultiplication are obtained.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Comment :

23 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T12:28:25Z