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.
The Bloch Space of M-Harmonic Functions on Bounded Symmetric Domains.
The boundary Harnack principle for the fractional Laplacian
We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.
The boundary value problem for Dirac-harmonic maps
Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...
The boundary-value problems for Laplace equation and domains with nonsmooth boundary
Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.
The Bremermann-Dirichlet problem for -plurisubharmonic functions
The Brothers Riesz theorem in and Laplace series.
The Cauchy transform of continuous linear functionals and projections on the weighted spaces of analytic functions.
The classification problem for the capacities associated with the Besov and Triebel-Lizorkin spaces
The complex Monge-Ampère operator in hyperconvex domains
The Convergence of Even Degree Spline Collocation Solution for Potential Problems in Smooth Domains of the Plane.