A Phragmén-Lindelöf Type Theorem for a Certain Class of Generalized Subharmonic Functions.
A remark on gradients of harmonic functions.
In any C1,s domain, there is nonzero harmonic function C1 continuous up to the boundary such that the function and its gradient on the boundary vanish on a set of positive measure.
A uniform boundary Harnack inequality on non-tangentially accessible domains.
A uniqueness theorem for invariantly harmonic functions in the unit ball of Cn.
We prove a boundary uniqueness theorem for harmonic functions with respect to Bergman metric in the unit ball of Cn and give an application to a Runge type approximation theorem for such functions.
Analogies entre espaces hyperboliques réels et l’arbre de Bruhat-Tits sur
Angular limits of double layer potentials
Applications of geometric measure theory to the study of Gauss- Weierstrass and Poisson integrals.
Asymptotic behavior of the invariant measure for a diffusion related to an NA group
On a Lie group NA that is a split extension of a nilpotent Lie group N by a one-parameter group of automorphisms A, the heat semigroup generated by a second order subelliptic left-invariant operator is considered. Under natural conditions there is a -invariant measure m on N, i.e. . Precise asymptotics of m at infinity is given for a large class of operators with Y₀,...,Yₘ generating the Lie algebra of S.
Boundary behavior of subharmonic functions in nontangential accessible domains
The following results concerning boundary behavior of subharmonic functions in the unit ball of are generalized to nontangential accessible domains in the sense of Jerison and Kenig [7]: (i) The classical theorem of Littlewood on the radial limits. (ii) Ziomek’s theorem on the -nontangential limits. (iii) The localized version of the above two results and nontangential limits of Green potentials under a certain nontangential condition.
Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains
Boundary behaviour of harmonic functions in a half-space and brownian motion
Let be harmonic in the half-space , . We show that can have a fine limit at almost every point of the unit cubs in but fail to have a nontangential limit at any point of the cube. The method is probabilistic and utilizes the equivalence between conditional Brownian motion limits and fine limits at the boundary.In it is known that the Hardy classes , , may be described in terms of the integrability of the nontangential maximal function, or, alternatively, in terms of the integrability...
Boundary behaviour of positive harmonic functions on Lipschitz domains.
Boundary limits of Green's potentials along curves II. Lipschitz domains
Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball.
Boundary properties of first-order partial derivatives of the Poisson integral for the half-space .
Boundary properties of second-order partial derivatives of the Poisson integral for a half-space .
Boundary Value Characterizations for Weighted Hardy Spaces of Harmonic Functions.
Cauchy-Szegö integrals for systems of harmonic functions
Comportement non-tangentiel et comportement brownien des fonctions harmoniques dans un demi-espace. Démonstration probabiliste d'un théorème de Calderon et Stein
Constructions de fonctions holomorphes bornées