Tangential boundary limits and exceptional sets for holomorphic functions in Dirichlet-type spaces.
The Bergman projection on harmonic functions
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 Bremermann-Dirichlet problem for -plurisubharmonic functions
The complex Monge-Ampère operator in hyperconvex domains
The Definition of Energy in Non-Symmetric Translation Invariant Dirichlet Spaces.
The Dirchlet Problem for a Complex Monge-Ampère Equation.
The Dirichlet space: a survey.
The Fekete-Szegő theorem with splitting conditions: Part I
The Fekete-Szegő theorem with splitting conditions: Part II
The finite integral transform method for a parabolic differential equation on a graph.
The form boundedness criterion for the relativistic Schrödinger operator
We establish necessary and sufficient conditions on the real- or complex-valued potential defined on for the relativistic Schrödinger operator to be bounded as an operator from the Sobolev space to its dual .
The Functional Equation
The gradient lemma
We show that if a decreasing sequence of subharmonic functions converges to a function in then the convergence is in .
The Green formula and HP Spaces on trees.
The Hölder duality for harmonic functions
The homogeneous transfinite diameter of a compact subset of
Let K be a compact subset of . A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of is computed.
The image of a finely holomorphic map is pluripolar
We prove that the image of a finely holomorphic map on a fine domain in ℂ is a pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic functions.