Inverse mean value property of harmonic functions (Corrigendum).
L2-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.
Landau's theorem for p-harmonic mappings in several variables
A 2p-times continuously differentiable complex-valued function f = u + iv in a domain D ⊆ ℂ is p-harmonic if f satisfies the p-harmonic equation , where p (≥ 1) is a positive integer and Δ represents the complex Laplacian operator. If Ω ⊂ ℂⁿ is a domain, then a function is said to be p-harmonic in Ω if each component function (i∈ 1,...,m) of is p-harmonic with respect to each variable separately. In this paper, we prove Landau and Bloch’s theorem for a class of p-harmonic mappings f from...
Le compactifié de Martin d’un domaine Lipschitzien borné dans
Level sets of polynomials in several real variables.
Lewy's theorem fails in higher dimensions.
Limites de quotients de fonctions harmoniques et espaces de Hardy associés à une marche aléatoire sur un groupe abélien
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.
Littlewood-Paley type inequalities for -harmonic functions.
Littlewood-Paley Type Inequalities for M-harmonic Functions
Local inequalities for plurisubharmonic functions.
Lp continuity of projectors of weighted harmonic Bergman spaces.
Majorantes surharmoniques minimales d'une fonction continue
Soit , ouvert de et , continue. On dit qu’une majorante surharmonique de dans est minimale si cette majorante surharmonique est harmonique dans l’ensemble (ouvert) où elle diffère de . Beaucoup de propriétés de ces fonctions sont semblables à celles des fonctions harmoniques (lesquelles correspondent à ) ; par exemple la famille entière est uniformément équicontinue dans chaque partie compacte de , relativement à la structure uniforme de . On traite le problème de Dirichlet : détermination...
Martin boundary for Schrödinger operators with singularity.
Maximal Weak-Type Inequality for Orthogonal Harmonic Functions and Martingales
Assume that u, v are conjugate harmonic functions on the unit disc of ℂ, normalized so that u(0) = v(0) = 0. Let u*, |v|* stand for the one- and two-sided Brownian maxima of u and v, respectively. The paper contains the proof of the sharp weak-type estimate ℙ(|v|* ≥ 1)≤ (1 + 1/3² + 1/5² + 1/7² + ...)/(1 - 1/3² + 1/5² - 1/7² + ...) 𝔼u*. Actually, this estimate is shown to be true in the more general setting of differentially subordinate harmonic functions defined...
Maximum principles for subharmonic functions.
Mean value densities for temperatures
A positive measurable function K on a domain D in is called a mean value density for temperatures if for all temperatures u on D̅. We construct such a density for some domains. The existence of a bounded density and a density which is bounded away from zero on D is also discussed.
Mean value theorems for harmonic and holomorphic functions on bounded symmetric domains.