Jorge Hounie

On The L2 continuity of pseudo_differential operators

Generalisation et unification des resultats de continuite relatifs aux operateurs pseudodifferentiels. Application des techniques de Coifman-Meyer et du principe de quasi-orthogonalite de Stein-Meyer

Uniqueness and Nonexistence Theorems for Hypersurfaces with Hr = 0

We use the Maximum Principle to derive theorems of uniqueness and nonexistence for embedded, multiply connected and compact hypersurfaces with boundaries in parallel hyperplanes, which satisfy the geometric property Hr = 0.

Local solvability for a class of differential complexes

In 1983 F. Treves IT1] initiated the study of the local solvability for the class of differential complexes defined by a smooth, locally integrable structure of rank n in a n + l . If Z denotes a local first integral of the structure, Treves conjectured that the vanishing of the local cohomology in degree q of such a differential complex would be related to the vanishing of the singular homology of the sets Z = const, in dimension q 1 . It is the purpose of this article to complete the proof of this conjecture in its full generality.

A sphere theorem for a class of Reinhardt domains with constant Levi curvature

Abstract We prove that a bounded Reinhardt domain of ℂ n+1 with C 2 boundary of constant Levi curvature with rotational symmetry in two complementary sets of variables is a ball. 2000 Mathematics Subject Classification: 53A07, 53O42; 35J70, 35B50, 32T99.

An F. and M. Riesz theorem for planar vector fields

Abstract. We prove that solutions of the homogeneous equation Lu=0, where L is a locally integrable vector field with smooth coefficients in two variables possess the F. and M. Riesz property. That is, if

Local integrability of Mizohata structures

\Omega

On the local solvability of semilinear equations

is an open subset of the plane with smooth boundary,

The Mizohata structure on the sphere

u\in C^1(\Omega)

Radó’s theorem for locally solvable vector fields

satisfiesLu=0 on

Uniqueness for locally integrable solutions of overdetermined systems

\Omega