Title :

Bilinear oscillatory integrals and boundedness for new bilinear multipliers

Author(s) :

Bernicot, Frederic [Auteur]
Laboratoire de Mathématiques d'Orsay [LMO]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Germain, Pierre [Auteur]
Courant Institute of Mathematical Sciences [New York] [CIMS]

Journal title :

Advances in Mathematics

Pages :

1739-1785

Publisher :

Elsevier

Publication date :

2010

ISSN :

0001-8708

English keyword(s) :

Bilinear operators
oscillatory integrals

HAL domain(s) :

Mathématiques [math]/Analyse classique [math.CA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger ; ...
Show more >We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger ; this extends the well-known linear theory of oscillatory integral in some directions. The proof relies on a combination of time-frequency analysis of Coifman-Meyer type with stationary and non-stationary phase estimates. As a consequence of this analysis, we obtain Lebesgue estimates for new bilinear multipliers defined by non-smooth symbols.Show less >

Language :

Anglais

Popular science :

Non

Comment :

35 pages, 3 figures

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL