no. 2
Theory of Bessel potentials. III: Potentials on regular manifolds
Annales de l'Institut Fourier, Tome 19 (1969) no. 2, pp. 279-338.

On étudie ici les potentiels besseliens sur des variétés riemanniennes de classe C ∞ bordées ou ouvertes. Soient : M une variété n-dimensionnelle et N une sous-variété de M de dimension k. On donne des conditions suffisantes pour que : 1) la restriction à N d’un potentiel α sur M soit un potentiel d’ordre α-n-k 2 sur N ; 2) un potentiel d’ordre α-n-k 2 sur N admette une extension à un potentiel d’ordre α sur M. On prouve aussi que pour une variété bordée M la restriction à son intérieur M i est un isomorphisme isométrique entre l’espace des potentiels d’ordre α sur M, et l’espace des potentiels d’ordre α sur M i .

In this paper Bessel potentials on C ∞ -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-n-k 2 on N ; 2) any potential of order α-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 between the spaces of potentials of order α on M and M i respectively.

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     title = {Theory of {Bessel} potentials. {III:} {Potentials} on regular manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {279--338},
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     year = {1969},
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Adams, Robert; Aronszajn, Nachman; Hanna, M. S. Theory of Bessel potentials. III: Potentials on regular manifolds. Annales de l'Institut Fourier, Tome 19 (1969) no. 2, pp. 279-338. doi : 10.5802/aif.328. https://aif.centre-mersenne.org/articles/10.5802/aif.328/

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