Lewy's theorem fails in higher dimensions.
Limit sets of plurisubharmonic functions.
Limites de quotients de fonctions harmoniques et espaces de Hardy associés à une marche aléatoire sur un groupe abélien
Lindelöf theorems for monotone Sobolev functions.
Linéarisation de la notion de convexité par rapport à un ensemble de fonctions
Liouville theorem for Dunkl polyharmonic functions.
Liouville theorems based on symmetric diffusions
Liouville type theorems for mappings with bounded (co)-distortion
We obtain Liouville type theorems for mappings with bounded -distorsion between Riemannian manifolds. Besides these mappings, we introduce and study a new class, which we call mappings with bounded -codistorsion.
Liouville type theorems for φ-subharmonic functions.
In this paper we present some Liouville type theorems for solutions of differential inequalities involving the φ-Laplacian. Our results, in particular, improve and generalize known results for the Laplacian and the p-Laplacian, and are new even in these cases. Phragmen-Lindeloff type results, and a weak form of the Omori-Yau maximum principle are also discussed.
Liouville's theorem and the restricted mean property for biharmonic functions.
Lipschitz conditions on the modulus of a harmonic function.
Lipschitz spaces of holomorphic and pluriharmonic functions on bounded symmetric domains in (N>1)
Littlewood-Paley type inequalities for -harmonic functions.
Littlewood-Paley Type Inequalities for M-harmonic Functions
Littlewood-Paley-Stein theory on Cn and Weyl multipliers.
Local admissible convergence of harmonic functions on non-homogeneous trees
We prove admissible convergence to the boundary of functions that are harmonic on a subset of a non-homogeneous tree equipped with a transition operator that satisfies uniform bounds suitable for transience. The approach is based on a discrete Green formula, suitable estimates for the Green and Poisson kernel and an analogue of the Lusin area function.
Local Fatou theorem and the density of energy on manifolds of negative curvature.
Local inequalities for plurisubharmonic functions.
Local property of Dirichlet forms and diffusions on general state spaces.
Logarithmic capacity is not subadditive – a fine topology approach
In Landkof’s monograph [8, p. 213] it is asserted that logarithmic capacity is strongly subadditive, and therefore that it is a Choquet capacity. An example demonstrating that logarithmic capacity is not even subadditive can be found e.gi̇n [6, Example 7.20], see also [3, p. 803]. In this paper we will show this fact with the help of the fine topology in potential theory.