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Inversion of potentials in rn with the aid of Gauss-Weierstrass integrals

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Literature cited

  1. V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  2. S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  3. P. I. Lizorkin, “Operators connected with fractional differentiation, and classes of differentiable functions,” Trudy Mat. Inst. Akad. Nauk SSSR,117, 212–243 (1972).

    Google Scholar 

  4. A. Marchaud, “Sur les derivees et sur les differences des fonctions,” J. Math. Pures Appl.,6, 337–425 (1927).

    Google Scholar 

  5. S. G. Samko, “On spaces of Riesz potentials,” Izv. Akad. Nauk SSSR, Ser. Mat.,40, No. 5, 1143–1172 (1976).

    Google Scholar 

  6. V. A. Nogin, “Inversion of Bessel potentials by means of hypersingular integrals,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 57–65 (1985).

    Google Scholar 

  7. R. J. Bagby, “A characterization of Riesz potentials and an inversion formula,” Indiana Univ. Math. J.,29, No. 4, 581–595 (1980).

    Google Scholar 

  8. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press (1971).

  9. 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).

    Google Scholar 

  10. 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).

    Google Scholar 

  11. R. Johnson, “Temperatures, Riesz potentials, and the Lipschitz spaces of Herz,” Proc. London Math. Soc. (3),27, 290–316 (1973).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 41, No. 1, pp. 34–42, January, 1987.

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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

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  • DOI: https://doi.org/10.1007/BF01159524

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