On étudie ici les potentiels besseliens sur des variétés riemanniennes de classe bordées ou ouvertes. Soient : une variété -dimensionnelle et une sous-variété de de dimension . On donne des conditions suffisantes pour que : 1) la restriction à d’un potentiel sur soit un potentiel d’ordre sur ; 2) un potentiel d’ordre sur admette une extension à un potentiel d’ordre sur . On prouve aussi que pour une variété bordée la restriction à son intérieur est un isomorphisme isométrique entre l’espace des potentiels d’ordre sur , et l’espace des potentiels d’ordre sur .
In this paper Bessel potentials on -Riemannian manifolds (open or bordered) are studied. Let be an -dimensional manifold, and a submanifold of of dimension . Sufficient conditions are given for: 1) the restriction to of any potential of order on to be a potential of order on ; 2) any potential of order on to be extendable to a potential of order on . It is also proved that for a bordered manifold the restriction to its interior is an isometric isomorphism between the spaces of potentials of order on and respectively.
@article{AIF_1969__19_2_279_0, author = {Adams, Robert and Aronszajn, Nachman and Hanna, M. S.}, title = {Theory of {Bessel} potentials. {III:} {Potentials} on regular manifolds}, journal = {Annales de l'Institut Fourier}, pages = {279--338}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {19}, number = {2}, year = {1969}, doi = {10.5802/aif.328}, mrnumber = {54 #915}, zbl = {0176.09902}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.328/} }
TY - JOUR AU - Adams, Robert AU - Aronszajn, Nachman AU - Hanna, M. S. TI - Theory of Bessel potentials. III: Potentials on regular manifolds JO - Annales de l'Institut Fourier PY - 1969 SP - 279 EP - 338 VL - 19 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.328/ DO - 10.5802/aif.328 LA - en ID - AIF_1969__19_2_279_0 ER -
%0 Journal Article %A Adams, Robert %A Aronszajn, Nachman %A Hanna, M. S. %T Theory of Bessel potentials. III: Potentials on regular manifolds %J Annales de l'Institut Fourier %D 1969 %P 279-338 %V 19 %N 2 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.328/ %R 10.5802/aif.328 %G en %F AIF_1969__19_2_279_0
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. http://archive.numdam.org/articles/10.5802/aif.328/
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