Some Caccioppoli estimates for differential forms.
Some characterizations of harmonic Bloch and Besov spaces
The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic --Bloch space and characterize it in terms of and where is a majorant. Similar results are extended to harmonic little --Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G. Ren, U. Kähler (2005).
Some constructions of biharmonic maps on the warped product manifolds
In this paper, we characterize a class of biharmonic maps from and between product manifolds in terms of the warping function. Examples are constructed when one of the factors is either Euclidean space or sphere.
Some Dirichlet spaces obtained by subordinate reflected diffusions.
In this paper we want to show how well-known results from the theory of (regular) elliptic boundary value problems, function spaces and interpolation, subordination in the sense of Bochner and Dirichlet forms can be combined and how one can thus get some new aspects in each of these fields.
Some estimates of integrals with a composition operator.
Some examples concerning applicability of the Fredholm-Radon method in potential theory
Simple examples of bounded domains are considered for which the presence of peculiar corners and edges in the boundary causes that the double layer potential operator acting on the space of all continuous functions on can for no value of the parameter be approximated (in the sub-norm) by means of operators of the form (where is the identity operator and is a compact linear operator) with a deviation less then ; on the other hand, such approximability turns out to be possible for...
Some non-linear function theoretic properties of Riemannian manifolds.
We study the appropriate versions of parabolicity stochastic completeness and related Liouville properties for a general class of operators which include the p-Laplace operator, and the non linear singular operators in non-diagonal form considered by J. Serrin and collaborators.
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.