Inverse mean value property of harmonic functions.
Inverse mean value property of harmonic functions (Corrigendum).
Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings
We extend the Rado-Choquet-Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado-Choquet-Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.
Limites de quotients de fonctions harmoniques et espaces de Hardy associés à une marche aléatoire sur un groupe abélien
Lipschitz conditions on the modulus of a harmonic function.
Lösung des Dirichlet Problems bei Jordangebieten mit analytischem Rand durch Interpolation.
Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group
Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group
On the domain S_a = {(x,e^b): x ∈ N, b ∈ ℝ, b > a} where N is a simply connected nilpotent Lie group, a certain N-left-invariant, second order, degenerate elliptic operator L is considered. N × {e^a} is the Poisson boundary for L-harmonic functions F, i.e. F is the Poisson integral F(xe^b) = ʃ_N f(xy)dμ^b_a(x), for an f in L^∞(N). The main theorem of the paper asserts that the maximal function M^a f(x) = sup{|ʃf(xy)dμ_a^b(y)| : b > a} is of weak type (1,1).
Maximal functions related to subelliptic operators with polynomially growing coefficients.
Maximum Principles for Minimal Surfaces and for Surfaces of Continuous Mean Curvature.
Mean values and harmonic functions.
Multipliers of the Vanishing Hardy Classes
New generalizations of the Poisson kernel.
Nonbasic harmonic maps onto convex wedges
We construct a nonbasic harmonic mapping of the unit disk onto a convex wedge. This mapping satisfies the partial differential equation where a(z) is a nontrivial extreme point of the unit ball of .
Non-subharmonicity of the Hausdorff distance
Si dimostra con esempi che la distanza di Hausdorff-Carathéodory fra i valori di funzioni multivoche, analitiche secondo Oka, non è subarmonica.
Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian
The relation between the Jacobian and the orders of a linear invariant family of locally univalent harmonic mapping in the plane is studied. The new order (called the strong order) of a linear invariant family is defined and the relations between order and strong order are established.
On a generalized asymptotic mean value property.
On a generalized logarithmic kernel and its potentials
On a generalized reflection law for functions satisfying the Helmholtz equation.
On a question of T. Sheil-Small regarding valency of harmonic maps
The aim of this work is to answer positively a more general question than the following which is due to T. Sheil-Small: Does the harmonic extension in the open unit disc of a mapping f from the unit circle into itself of the form f(eit) = eiϕ(t), 0 ≤ t ≤ 2π, where ϕ is a continuously non-decreasing function that satisfies ϕ(2π)−ϕ(0) = 2Nπ, assume every value finitely many times in the disc?