Displaying similar documents to “Theory of Bessel potentials. I”

Functional spaces and functional completion

Nachman Aronszajn, K. T. Smith (1956)

Annales de l'institut Fourier

Similarity:

Dans le travail présent nous considérons des classes linéaires fonctionnelles ℱ dont les fonctions sont définies sur un ensemble de base à l’exception d’un ensemble A ⊂ ℰ appartenant à une classe 𝔞 d’ensemble ( A variant avec la fonction). Les notions d’une classe fonctionnelle normée et d’un espace fonctionnel sont introduites ensuite. Notre problème central est de trouver une complétion fonctionnelle ℱ ˜ d’une classe fonctionnelle normée ℱ (c’est-à-dire un espace fonctionnel complet ℱ ˜ dont...

A new setting for potential theory. I

Kai Lai Chung, K. Murali Rao (1980)

Annales de l'institut Fourier

Similarity:

We consider a transient Hunt process in which the potential density u satisfies the conditions: (a) for each x , u ( x , y ) - 1 is finite continuous in y ; (b) u ( x , y ) = + ∞ iff x = y . In earlier papers Chung established an equilibrium principle, and Rao obtained a Riesz of decomposition for excessive functions. We now begin a deeper study under these conditions, including the uniqueness of the decomposition and Hunt’s hypothesis (B).

A Whitney extension theorem in L p and Besov spaces

Alf Jonsson, Hans Wallin (1978)

Annales de l'institut Fourier

Similarity:

The classical Whitney extension theorem states that every function in Lip ( β , F ) , F ⊂ R n , F closed, k < β ≤ k + 1 , k a non-negative integer, can be extended to a function in Lip ( β , R n ) . Her Lip ( β , F ) stands for the class of functions which on F have continuous partial derivatives up to order k satisfying certain Lipschitz conditions in the supremum norm. We formulate and prove a similar theorem in the L p -norm. The restrictions to R d , d < n , of the Bessel potential spaces in R n and the Besov or generalized Lipschitz...

Thin sets in nonlinear potential theory

Lars-Inge Hedberg, Thomas H. Wolff (1983)

Annales de l'institut Fourier

Similarity:

Let L α q ( R D ) , α > 0 , 1 < q < ∞ , denote the space of Bessel potentials f = G α * g , g ∈ L q , with norm ∥ f ∥ α , q = ∥ g ∥ q . For α integer L α q can be identified with the Sobolev space H α , q . One can associate a potential theory to these spaces much in the same way as classical potential theory is associated to the space H 1 ; 2 , and a considerable part of the theory was carried over to this more general context around 1970. There were difficulties extending the theory of thin sets, however. By means of a new inequality, which characterizes the...