A bilinear pseudodifferential calculus.

Frederic Bernicot (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the bilinear Hilbert transform. We give a description of the action of our bilinear operators on Sobolev spaces. These classes also have a ''nice'' behavior through the transposition and the composition operations that we will present.

Mots clés: multilinear pseudodifferential calculus; time-frequency analysis; asymptotic expansion

Domaines: Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]

Frederic Bernicot. A bilinear pseudodifferential calculus.. Journal of Geometric Analysis, 2010, 20, pp.39-62. ⟨hal-00232882v2⟩