Some old and new applications of Choquet theory in potential theory
Some orthogonal decompositions of Sobolev spaces and applications
Two kinds of orthogonal decompositions of the Sobolev space W̊₂¹ and hence also of for bounded domains are given. They originate from a decomposition of W̊₂¹ into the orthogonal sum of the subspace of the -solenoidal functions, k ≥ 1, and its explicitly given orthogonal complement. This decomposition is developed in the real as well as in the complex case. For the solenoidal subspace (k = 0) the decomposition appears in a little different form. In the second kind decomposition the -solenoidal...
Some properties and applications of harmonic mappings
Some properties and characterizations of -normal functions.
Some properties of a generalized heat potential (Preliminary communication)
Some properties of composition operators on the Dirichlet space.
Some properties of functions with bounded mean oscillation
Some properties of positive superharmonic functions
Some properties of potentials of signed measures (Preliminary communication)
Some properties of the extreme values of infinity-harmonic functions.
Some properties of the reduced modulus in space.
Some properties of weighted hyperbolic polynomials.
Some properties of α-harmonic measure
The α-harmonic measure is the hitting distribution of symmetric α-stable processes upon exiting an open set in ℝⁿ (0 < α < 2, n ≥ 2). It can also be defined in the context of Riesz potential theory and the fractional Laplacian. We prove some geometric estimates for α-harmonic measure.
Some capacities and applications - the lemma on mixed derivatives revisited
Some remarks on largest subharmonic minorants.
Some Remarks on Strict Potentials.
Some remarks on the existence of a resolvent
Noting that a resolvent is associated with a convolution kernel satisfying the domination principle if and only if has the dominated convergence property, we give some remarks on the existence of a resolvent.
Some results on thin sets in a half plane
When one is restricted to a Stolz domain in a half plane we prove that internal thinness of a set at the origin structly implies minimal thinness there. Furthermore this result extends to the half plane itself. We also work out some relations among the concepts of minimal thinness, semi-thinness and finite logarithmic length. Finally we show that a theorem of Ahlfors and Heins can be improved.
Some simple proofs in holomorphic spectral theory
This paper gives some very elementary proofs of results of Aupetit, Ransford and others on the variation of the spectral radius of a holomorphic family of elements in a Banach algebra. There is also some brief discussion of a notorious unsolved problem in automatic continuity theory.
Some uniqueness results for Bernoulli interior free-boundary problems in convex domains.