Potentiels besséliens
Annales de l'Institut Fourier, Volume 15 (1965) no. 1, pp. 43-58.

On donne une revue des propriétés de certaines classes des potentiels besséliens dans R n . On obtient leurs définitions directes (ne faisant pas appel à leurs représentations comme potentiels). On étudie leurs restrictions à certains sous-ensembles de R n , notamment aux hyperplans k-dimensionnels et aux sous-ensembles ouverts. On omet ici, par manque de place la question des restrictions aux sous-variétés différentiables.

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     title = {Potentiels bess\'eliens},
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Aronszajn, Nachman. Potentiels besséliens. Annales de l'Institut Fourier, Volume 15 (1965) no. 1, pp. 43-58. doi : 10.5802/aif.194. http://www.numdam.org/articles/10.5802/aif.194/

[1] N. Aronszajn and K. T. Smith, Functional spaces and functional completion, Ann. de l'Inst. Fourier, Grenoble, 6 (1956), 125-185. | Numdam | MR | Zbl

[2] N. Aronszajn and K. T. Smith, Theory of Bessel potentials, Part I, Ann. de l'Inst. Fourier, 11 (1961), 385-475. | Numdam | MR | Zbl

[3] R. Adams, N. Aronszajn and K. T. Smith, Theory of Bessel potentials, Part II (à paraître prochainement). | Numdam | Zbl

[4] N. Aronszajn, Fuad Mulla and P. Szeptycki, On spaces of potentials connected with Lp classes, Ann. de l'Inst. Fourier, 13 (1963), 211-306. | Numdam | Zbl

[5] O. V. Besov, On a family of functional spaces. Theorems about restrictions and extensions, Dokl. Ak. Nauk SSSR, 126, 6 (1959), 1163-1165. | Zbl

[6] A. P. Calderon, Lebesgue spaces of differentiable functions and distributions, Proc. of Symp. in Pure Math., vol. IV, Partial Differential Equations (1961), 33-49. | MR | Zbl

[7] A. P. Calderon, Intermediate spaces and interpolation, Reports of the Conference on Functional Analysis, Warsaw, 1960.

[8] W. H. Fleming, Functions whose partial derivatives are measures, Bull. Am. Math. Soc., 64 (1958), 364-366. | MR | Zbl

[9] E. Gagliardo, Caratterizzazioni della tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Rendiconti Sem. Mat. Padova, 27 (1957), 284-305. | Numdam | MR | Zbl

[10] M. R. Hestenes, Extension of the range of a differentiable function, Duke Math. Journ., 8 (1941), 183-192. | JFM | MR | Zbl

[11] L. Lichtenstein, Eine elementare Bemerkung zur reelen Analysis, Math. Zeit., 30 (1929), 794-795. | JFM

[12] J. L. Lions, Une construction d'espaces d'interpolation, C. R. Ac. Sci., Paris, 251 (1961), 1853-1855. | Zbl

[13] S. M. Nikolskii, Theorems about restrictions, extensions, and approximations of differentiable functions of several variables (survey article), Usp. Mat. Nauk., 16, 5 (1961), 63-114.

[14] R. T. Seeley, Extension of C∞ functions defined in a half-space. A paraître prochainement dans Proc. Am. Math. Soc. | Zbl

[15] L. I. Slobodeckii, Spaces of S. L. Soblev of fractional order, Dokl. Akad. Nauk. SSSR., 118 (1958), 243-246. | Zbl

[16] E. M. Stein, The characterization of functions arising as potentials I, Bull. Amer. Math. Soc., 68 (1961), 102-104. | MR | Zbl

[17] E. M. Stein, The characterization of functions arising as potentials II, Bull. Amer. Math. Soc., 68 (1962), 577-584. | MR | Zbl

[18] P. Szeptycki, On restrictions of functions in the spaces Pϑ,p and Bϑ,p. Technical Report 5 Univ. Kansas. A paraître dans Proc. Am. Math. Soc. | Zbl

[19] M. H. Taibleson, Smoothness and differentiability conditions for functions and distributions in En. Dissertation, Univ. Chicago, 1962.

[20] J. L. Lions, J. Peetre, Inst. des Hautes Études Sci., 19 (1964). | Numdam | Zbl

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