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It is shown that the methods developed in an earlier paper of the author about a Dirichlet problem for the Silov boundary [Annales Inst. Fourier, 11 (1961)] lead in a new and natural way to the most important results about the convergence of positive linear operators on spaces of continuous functions defined on a compact space. Choquet’s notion of an adapted space of continuous functions in connection with results of Mokobodzki-Sibony opens the possibility of extending these results to the case...

Théorie non-linéaire du potentiel : un principe unifié de domination et du maximum et quelques applications

Claude Dellacherie (1991)

Séminaire de probabilités de Strasbourg

Thinness and the heat equation

Ivan Netuka (1974)

Časopis pro pěstování matematiky

Topological countability in Brelot potential theory

Thomas E. Armstrong (1974)

Annales de l'institut Fourier

Let $U$ be a domain of type $H$ in a Brelot potential theory. A compact $K$ in $U$ is a $G_{δ}$ in $U$ iff $U - K$ has at most countably many components. If $F$ is a relatively closed locally polar subset of $U$ , any $G_{δ}$ in $F$ is a $G_{δ}$ in $U$ . If $V$ is a domain in $U$ , all Borel subsets of $\partial V \cap U$ are Baire even if $\partial V \cap U$ is not metrizable. The known results concerning equivalences between weak thinness, thinness, and strong thinness of a set $A$ at a point $x \notin A$ are extended from the case where ${x}$ is a $G_{δ}$ to the cases in which $A$ meets only countably...

Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain

Bjorn Dahlbert (1980)

Studia Mathematica

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The Dirichlet Problem for Sublaplacians on Nilpotent Gruops - Geometric Criteria For Regularity.

The General Riesz Decomposition and the Specific Order of Excessive Functions.

The Harmonie Space Associated with a "Reasonable" Standard Process.

The insertion of $G_{δ}$ sets and fine topologies

The insertion of regular sets in potential theory

The Lusin-Menchoff property of fine topologies

The resolvent for a convolution kernel satisfying the domination principle

The weak Dirichlet problem.

Théorème de Keldych dans la théorie axiomatique de Bauer des fonctions harmoniques

Theorems of Korovkin type for adapted spaces

Théorie non-linéaire du potentiel : un principe unifié de domination et du maximum et quelques applications

Thinness and the heat equation

Topological countability in Brelot potential theory

Topologie fine dans les espaces harmoniques

Tusk type conditions and thinness for the parabolic operator of order ...

Two applications of an integral formula

Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain

When finely continuous functions are of the first class of Baire

Wiener's Criterion in Potential Theory with Applications to Nilpotent Lie Groups.

Wiener's test of thinness in potential theory

Currently displaying 161 – 180 of 182