Theory of Bessel potentials. II

Robert Adams; Nachman Aronszajn; K. T. Smith

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

On spaces of potentials connected with $L^{p}$ classes

Nachman Aronszajn, Szeptycki P. (1963)

Annales de l'institut Fourier

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Dans le mémoire présent une méthode nouvelle est présentée pour la recherche des différentes classes de potentiels, associées aux classes $L^{p}$ . Cette méthode consiste dans l’établissement de formules intégrales appropriées, représentant les fonctions de ces classes. L’analyse des opérateurs intégraux donnés par ces formules permet d’obtenir tous les résultats. Dans le premier chapitre, on introduit les différentes normes sur l’espace $C_{0}^{\infty}$ qui, par complétion, donnent...

Construction and analysis of some convolution algebras

Arne Beurling (1964)

Annales de l'institut Fourier

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À une famille $Ω$ de fonctions positives $ω$ sur un groupe $G$ abélien localement compact, on associe l’ensemble $A^{2}$ des fonctions qui sont de carré sommable sur $G$ par rapport à $d x / ω (x)$ pour au moins un $ω \in Ω$ . Sous certaines conditions simples, portant sur $Ω$ , c’est une algèbre de convolution, contenue dans $L^{1} (G)$ . On étudie particulièrement le cas $G =$ droite réelle, $Ω =$ ensemble des fonctions paires, sommables, décroissantes sur $] 0, \infty [$ . Une caractérisation explicite de $\tilde{A}$ (ensemble des transformées de Fourier des $f \in A$ )...

Approximation of harmonic functions

Björn E. J. Dahlberg (1980)

Annales de l'institut Fourier

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Let $u$ be harmonic in a bounded domain $D$ with smooth boundary. We prove that if the boundary values of $u$ belong to $L^{p} (σ)$ , where $p \geq 2$ and $σ$ denotes the surface measure of $\partial D$ , then it is possible to approximate $u$ uniformly by function of bounded variation. An example is given that shows that this result does not extend to $p < 2$ .

Theory of Bessel potentials. III : potentials on regular manifolds

Robert Adams, Nachman Aronszajn, M. S. Hanna (1969)

Annales de l'institut Fourier

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In this paper Bessel potentials on $C^{\infty}$ -Riemannian manifolds (open or bordered) are studied. Let $M$ be an $n$ -dimensional manifold, and $N$ a submanifold of $M$ of dimension $k$ . Sufficient conditions are given for: 1) the restriction to $N$ of any potential of order $α$ on $M$ to be a potential of order $α - \frac{n - k}{2}$ on $N$ ; 2) any potential of order $α - \frac{n - k}{2}$ on $N$ to be extendable to a potential of order $α$ on $M$ . It is also proved that for a bordered manifold $M$ the restriction to its interior $M^{i}$ is an isometric isomorphism...

Two separation criteria for second order ordinary or partial differential operators

Richard C. Brown, Don B. Hinton (1999)

Mathematica Bohemica

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We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in $ℝ^{n}$ . Also, for symmetric second-order ordinary differential operators we show that ${lim sup}_{t \to c} {(p q^{'})}^{'} / q^{2} = θ < 2$ where $c$ is a singular point guarantees separation of $- {(p y^{'})}^{'} + q y$ on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that $- Δ y + q y$ is separated on its minimal domain if $q$ is superharmonic. For $n = 1$ the...

A mixed boundary value problem for the Laplace equation in an angle (2nd part)

Alfredo Lorenzi (1976)

Rendiconti del Seminario Matematico della Università di Padova

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

On spaces of potentials connected with L p classes

Construction and analysis of some convolution algebras

Approximation of harmonic functions

Theory of Bessel potentials. III : potentials on regular manifolds

Two separation criteria for second order ordinary or partial differential operators

A mixed boundary value problem for the Laplace equation in an angle (2nd part)

On spaces of potentials connected with $L^{p}$ classes