Characterization of best harmonic and superharmonic L1-approximations.
Characterization of global Phragmén-Lindelöf conditions for algebraic varieties by limit varieties only
For algebraic surfaces, several global Phragmén-Lindelöf conditions are characterized in terms of conditions on their limit varieties. This shows that the hyperbolicity conditions that appeared in earlier geometric characterizations are redundant. The result is applied to the problem of existence of a continuous linear right inverse for constant coefficient partial differential operators in three variables in Beurling classes of ultradifferentiable functions.
Characterization of nuclear Fréchet spaces in which every bounded set is polar
Characterizations of balayages.
Characterizations of p-superharmonic functions on metric spaces
We show the equivalence of some different definitions of p-superharmonic functions given in the literature. We also provide several other characterizations of p-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also...
Charakterisierung von Produkten harmonischer Räume.
Choquet integrals in potential theory.
This is a survey of various applications of the notion of the Choquet integral to questions in Potential Theory, i.e. the integral of a function with respect to a non-additive set function on subsets of Euclidean n-space, capacity. The Choquet integral is, in a sense, a nonlinear extension of the standard Lebesgue integral with respect to the linear set function, measure. Applications include an integration principle for potentials, inequalities for maximal functions, stability for solutions to...
Choquetova teorie a Dirichletova úloha
Choquetova teorie kapacit
Classes de Bergman de fonctions harmoniques
Coarea integration in metric spaces
Let be a metric space with a doubling measure, be a boundedly compact metric space and be a Lebesgue precise mapping whose upper gradient belongs to the Lorentz space , . Let be a set of measure zero. Then for -a.e. , where is the -dimensional Hausdorff measure and is the -codimensional Hausdorff measure. This property is closely related to the coarea formula and implies a version of the Eilenberg inequality. The result relies on estimates of Hausdorff content of level sets...
Coefficient estimates and Landau-Bloch's constant for planar harmonic mappings.
Cohomologie des faisceaux de fonctions harmoniques
Commuting Toeplitz operators on the pluriharmonic Bergman space
We prove that two Toeplitz operators acting on the pluriharmonic Bergman space with radial symbol and pluriharmonic symbol respectively commute only in an obvious case.
Compactification associée à une résolvante
Comparison of Two Capacities in Cn.
Comparison Theorems on Dirichlet Norms and their Applications.
Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains
On a Lipschitz domain in , three theorems on harmonic functions are proved. The first (boundary Harnack principle) compares two positive harmonic functions at interior points near an open subset of the boundary where both functions vanish. The second extends some familiar geometric facts about the Poisson kernel on a sphere to the Poisson kernel on . The third theorem, on non-tangential limits of quotient of two positive harmonic functions in , generalizes Doob’s relative Fatou theorem on a...
Completeness and existence of bounded biharmonic functions on a riemannian manifold
A.S. Galbraith has communicated to us the following intriguing problem: does the completeness of a manifold imply, or is it implied by, the emptiness of the class of bounded nonharmonic biharmonic functions? Among all manifolds considered thus far in biharmonic classification theory (cf. Bibliography), those that are complete fail to carry -functions, and one might suspect that this is always the case. We shall show, however, that there do exist complete manifolds of any dimension that carry...