Painlevé' s Theorem and the Phragmén-Lindelöf Maximum Principle.
Parabolic Harnack inequality and local limit theorem for percolation clusters.
Parapolicity and existence of bounded biharmonic functions
Pointwise and locally uniform convergence of holomorphic and harmonic functions.
Pointwise and locally uniform convergence of holomorphic and harmonic functions
We shall characterize the sets of locally uniform convergence of pointwise convergent sequences. Results obtained for sequences of holomorphic functions by Hartogs and Rosenthal in 1928 will be generalized for many other sheaves of functions. In particular, our Hartogs-Rosenthal type theorem holds for the sheaf of solutions to the second order elliptic PDE's as well as it has applications to the theory of harmonic spaces.
Positive Schatten class Toeplitz operators on the ball
On the harmonic Bergman space of the ball, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten class operator in terms of averaging functions and Berezin transforms.
Positive Toeplitz operators between the pluriharmonic Bergman spaces
We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space into another for in terms of certain Carleson and vanishing Carleson measures.
Principe du minimum et préfaisceaux maximaux
Le faisceau des fonctions hyperharmoniques dans les ouverts de vérifie le principe du minimum et est maximal parmi les faisceaux de cônes convexes de fonctions s.c.i. vérifiant ce principe du minimum.On se donne plus généralement un espace localement dans lequel on définit différents principes du minimum, et on étudie la donnée d’un faisceau de cônes convexes de fonctions s.c.i. qui soit maximal par rapport à l’un de ces principes.On montre ainsi comment on peut caractériser certains de...
Problème de Neumann sur les espaces harmoniques.
Propriété restreinte de valeur moyenne caractérisant les fonctions harmoniques bornées sur un ouvert (selon D. Heath et S. Orey)