-boundedness and -compactness of a class of Fourier integral operators.
estimates for pseudodifferential operators
and Hölder estimates for pseudodifferential operators : sufficient conditions
Continuity in spaces and spaces of Hölder type is proved for pseudodifferential operators of order zero, under general conditions on the class of symbols. Applications to the regularity theory of some hypoelliptic operators are outlined.
-boundedness for pseudodifferential operators with non-smooth symbols and applications
Starting from a general formulation of the characterization by dyadic crowns of Sobolev spaces, the authors give a result of continuity for pseudodifferential operators whose symbol a(x,ξ) is non smooth with respect to x and whose derivatives with respect to ξ have a decay of order ρ with . The algebra property for some classes of weighted Sobolev spaces is proved and an application to multi - quasi - elliptic semilinear equations is given.
La condition de Hörmander-Kohn pour les opérateurs pseudo-différentiels
La série discrète de et les opérateurs pseudo-différentiels sur une demi-droite
Le problème de Cauchy ramifié semi-linéaire d'ordre deux
Lemme div-curl et renormalisation
Les opérateurs pseudo-différentiels classiques et leurs conjugués par changement de variable
Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group
Lie algebras of formal power series.
L'opérateur de temps-retard dans la théorie de la diffusion
Low regularity Cauchy theory for the water-waves problem: canals and swimming pools
The purpose of this talk is to present some recent results about the Cauchy theory of the gravity water waves equations (without surface tension). In particular, we clarify the theory as well in terms of regularity indexes for the initial conditions as fin terms of smoothness of the bottom of the domain (namely no regularity assumption is assumed on the bottom). Our main result is that, following the approach developed in [1, 2], after suitable para-linearizations, the system can be arranged into...
Lower bounds for pseudo-differential operators
Lower bounds for pseudo-differential operators
Lower bounds for pseudo-differential operators
This paper contains some new results on lower bounds for pseudo-differential operators whose symbols do not remain positive. Non-negativity of averages of the symbol on canonical images of the unit ball is sufficient to get a Gårding type inequality for Schrödinger operators with magnetic potential and one dimensional pseudo-differential operators.
Lp estimates for degenerate elliptic equations.
In this note we are going to address the question of when a second order differential operator is controlled by a subelliptic second order differential operator.