Surface integrals and harmonic functions.
Surfaces of minimum capacity for a knot
Symmetric and Zygmund measures in several variables
Let be a gauge function satisfying certain mid regularity conditions. A (signed) finite Borel measure is called -Zygmund if there exists a positive constant such that for any pair of adjacent cubes of the same size. Similarly, is called an - symmetric measure if there exists a positive constant such that for any pair of adjacent cubes of the same size, . We characterize Zygmund and symmetric measures in terms of their harmonic extensions. Also, we show that the quadratic condition...
Symmetric Harmonic Groups and Translation Invariant Dirichlet Spaces.
Symmetric reflected diffusions
Symmetry and Overdetermined Boundary Value Problems.
Symmetry for exterior elliptic problems and two conjectures in potential theory
Symmetry problems 2
Some symmetry problems are formulated and solved. New simple proofs are given for some symmetry problems studied earlier. One of the results is as follows: if a single-layer potential of a surface, homeomorphic to a sphere, with a constant charge density, is equal to c/|x| for all sufficiently large |x|, where c > 0 is a constant, then the surface is a sphere.
Systèmes doublement orthogonaux de fonctions holomorphes et applications
0. Introduction. Nous donnons ici une étude systématique des systèmes doublement orthogonaux "de Bergman" et leurs applications à certains aspects de l'analyse pluricomplexe: espaces de fonctions holomorphes, fonctions séparément analytiques. C'est en quelque sorte un article de synthèse. On y trouve cependant des démonstrations détaillées qui n'ont paru nulle part ailleurs.
Szegő projections for Hardy spaces of monogenic functions and applications.
Tangential boundary limits and exceptional sets for holomorphic functions in Dirichlet-type spaces.
Tangential limits of monotone Sobolev functions.
Temps locaux et l'intégrale d'aire de Lusin
Teoremi di confronto di tipo Harnack per funzioni armoniche in domini con frontiera hölderiana
Teoremi di media e formole di maggiorazione relative alle funzioni biarmoniche
The Absolute Continuity of Elliptic Measure Revisited.
The atomic decomposition of harmonic functions satisfying certain conditions of integrability.
The Berezin transform and operators on spaces of analytic functions
In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz operators 6....
The Bergman projection on harmonic functions
The Besov capacity in metric spaces
We study a capacity theory based on a definition of Hajłasz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are γ-medians, for which we also prove a new version of a Poincaré type inequality.