Deux généralisation du «théorèm des trois cercles» de Hadamard.
Différentiabilité des fonctions finement harmoniques.
Dirichlet finite biharmonic functions on the Poincaré N-ball.
Dirichlet problem with L-boundary data in contractible domains of Carnot groups
Let be a sub-laplacian on a stratified Lie group . In this paper we study the Dirichlet problem for with -boundary data, on domains which are contractible with respect to the natural dilations of . One of the main difficulties we face is the presence of non-regular boundary points for the usual Dirichlet problem for . A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces.
Discrete groups and thin sets.
Distribution function inequalities for the area integral
Distributions bi-sousharmoniques sur
L’object de ce travail est l’etude des fonctions fonctions localement sommable sur , vérifiant (où est Laplacien pris au sens des distributions) et que se comportent à l’infini comme des fonctions sousharmoniques. En parculier, nous caractérisons les fonctious qui sont à la fois bi-sousharmoniques et sousharmoniques.
Doubling conditions for harmonic measure in John domains
We introduce new classes of domains, i.e., semi-uniform domains and inner semi-uniform domains. Both of them are intermediate between the class of John domains and the class of uniform domains. Under the capacity density condition, we show that the harmonic measure of a John domain satisfies certain doubling conditions if and only if is a semi-uniform domain or an inner semi-uniform domain.