Literature cited
V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1981).
S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1977).
P. I. Lizorkin, “Operators connected with fractional differentiation, and classes of differentiable functions,” Trudy Mat. Inst. Akad. Nauk SSSR,117, 212–243 (1972).
A. Marchaud, “Sur les derivees et sur les differences des fonctions,” J. Math. Pures Appl.,6, 337–425 (1927).
S. G. Samko, “On spaces of Riesz potentials,” Izv. Akad. Nauk SSSR, Ser. Mat.,40, No. 5, 1143–1172 (1976).
V. A. Nogin, “Inversion of Bessel potentials by means of hypersingular integrals,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 57–65 (1985).
R. J. Bagby, “A characterization of Riesz potentials and an inversion formula,” Indiana Univ. Math. J.,29, No. 4, 581–595 (1980).
E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press (1971).
P. I. Lizorkin, “Generalized Liouville differentiation and the method of multipliers in the theory of imbeddings of classes of differentiable functions,” Tr. Mat. Inst. Akad. Nauk SSSR,105, 89–167 (1969).
M. H. Taibleson, “On the theory of Lipschitz spaces of distributions of Euclidean n-space. I. Principal properties,” J. Math. Mech.,13, No. 3, 407–479 (1964).
R. Johnson, “Temperatures, Riesz potentials, and the Lipschitz spaces of Herz,” Proc. London Math. Soc. (3),27, 290–316 (1973).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 41, No. 1, pp. 34–42, January, 1987.
Rights and permissions
About this article
Cite this article
Rubin, B.S. Inversion of potentials in rn with the aid of Gauss-Weierstrass integrals. Mathematical Notes of the Academy of Sciences of the USSR 41, 22–27 (1987). https://doi.org/10.1007/BF01159524
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01159524