Une construction de fonctions plurisousharmoniques nous permet, en utilisant les techniques de Hörmander, d’obtenir un résultat de -cohomologie à croissance. Les méthodes de B. Malgrange nous fournissent alors deux applications aux systèmes différentiels à coefficients constants.
We study unbounded harmonic functions for a second order differential operator on a homogeneous manifold of negative curvature which is a semidirect product of a nilpotent Lie group N and A = ℝ⁺. We prove that if F is harmonic and satisfies some growth condition then F has an asymptotic expansion as a → 0 with coefficients from 𝓓'(N). Then we single out a set of at most two of these coefficients which determine F. Then using asymptotic expansions we are able to prove some theorems...
Let , be elliptic operators with Hölder continuous coefficients on a bounded domain of class . There is a constant depending only on the Hölder norms of the coefficients of and its constant of ellipticity such thatwhere (resp. ) are the Green functions of (resp. ) on .
We prove universal overconvergence phenomena for harmonic functions on the real hyperbolic space.
The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros is extended to subharmonic functions in , having the Riesz masses on a ray.
In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.
Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions...
Some results of Bourgain on the radial variation of harmonic functions in the disk are extended to the setting of harmonic functions in upper half-spaces.