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Singular convolution operators with a discontinuous symbol

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Literature Cited

  1. F. D. Gakhov, Boundary Value Problems [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  2. N. I. Muskhelishvili, Singular Integral Equations [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  3. N. K. Karapetyants and S. G. Samko, “On the index of certain classes of integral operators,” Dokl. Akad. Nauk SSSR,194, No. 3, 504–507 (1970).

    Google Scholar 

  4. N. K. Karapetyants and S. G. Samko, “On the index of certain classes of integral operators,” Izv. Akad. Nauk ArmSSR, Ser. Matem.,8, No. 1, 26–40 (1973).

    Google Scholar 

  5. G. I. Savel'ev, “On a class of linear singular integral equations,” Trudy Novocherkassk. Politekh. Inst.,168, 3–10 (1960).

    Google Scholar 

  6. R. V. Duduchaea, “Discrete Wiener-Hopf equations in the spacel p with a weight,” Soob. Akad. Nauk GSSR,67, No. 1, 17–20 (1972).

    Google Scholar 

  7. N. K. Karapetyants and S. G. Samko, “On a class of convolution type integral equations, and its applications,” Izv. Akad. Nauk SSSR, Ser. Matem.,35, No. 3, 714–726 (1971).

    Google Scholar 

  8. M. A. Krasnosel'skii, P. P. Zabreiko, E. I. Pustyl'nik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  9. S. G. Mikhlin, “Singular intègral equations,” Usp. Matem. Nauk.111, No. 3, 29–112 (1948).

    Google Scholar 

  10. T. Carleman, L'intègrale de Fourier et questions qui se rattachent, Uppsala (1944).

  11. G. Hardy, J. Littlewood, and G. Polya, Inequalities [Russian translation], IL, Moscow (1948).

    Google Scholar 

  12. H. Kober, “On a theory of Schur and on fractional integrals of purely imaginary order,” Trans. Amer. Math. Soc.,50, 160–174 (1941).

    Google Scholar 

  13. M. J. Fisher, “Purely imaginary powers of certain differential operators. I,” Amer. J. Math.,93, No. 2, 452–478 (1971).

    Google Scholar 

  14. P. I. Lizorkin, “Generalized Liouville differentiation and the functional spaces L rp (En). Embedding theorems,” Matem. Sb.,60, No. 3, 325–352 (1963).

    Google Scholar 

  15. P. I. Lizorkin, “Generalized Liouville differentiation and the method of multipliers in the embedding theory of classes of differentiable functions,” Trudy Matem. Inst. Akad. Nauk SSSR,105, 89–167 (1969).

    Google Scholar 

  16. I. M. Gel'fand and G. E. Shilov, Spaces of Generalized Functions [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

  17. I. M. Gel'fand and G. E. Shilov, Generalized Functions and Operations [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  18. M. Arosajn and K. Smith, “Theory of Bessel potentials. I,” Ann. Inst. Fourier,XI, 385–475 (1961).

    Google Scholar 

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

    Google Scholar 

  20. S. G. Samko, “On the space Iα(Lp) of fractional integrals and on potential type operators,” Izv. Akad. Nauk ArmSSR, Ser. Matem.,8, No. 5, 359–383 (1973).

    Google Scholar 

  21. S. G. Samko, “On the integral modulus of continuity of potentials with densities that are summable on the real line with a weight,” in: Mathematical Analysis and Its Applications [in Russian], Izd. Rostov Univ., Rostov-on-Don (1969), pp. 175–184.

    Google Scholar 

  22. S. G. Mikhlin Multidimensional Singular Integrals and Integral Equations [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  23. I. Ts. Gokhberg and N. Ya. Krupnik, Introduction to the Theory of One-Dimentional Singular Integral Operators [in Russian], Shtiintsa, Kishinev (1973).

    Google Scholar 

  24. V. S. Rogozhin, The Theory of Noetherian Operators [in Russian], Izd. Rostov Univ., Rostov-on-Don (1973).

    Google Scholar 

  25. N. K. Karapetyants and S. G. Samko, “On discrete Wiener-Hopf operators with oscillatory coefficients,” Dokl. Akad. Nauk SSSR,200, No. 1, 17–21 (1971).

    Google Scholar 

  26. I. B. Simonenko, “Some general questions about the theory of the Riemann boundary value problem,” Izv. Akad. Nauk SSSR, Ser. Matem.,32, No. 5, 1138–1146 (1968).

    Google Scholar 

  27. H. Widom, “Singular integral equations in Lp,” Trans. Amer. Math. Soc.,97, No. 1, 131–160 (1960).

    Google Scholar 

  28. I. Ts. Gokhberg and I. A. Fel'dman, Convolution Equations and Projection Methods of Solving Them [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  29. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Ed. 4, Fizmatgiz, Moscow (1962).

    Google Scholar 

  30. I. Ts. Gokhberg and N. Ya. Krupnik, “On the spectrum of singular integral operators in the Lp space,” Studia Math.,31, No. 4, 347–362 (1968).

    Google Scholar 

  31. B. S. Rubin, “On the spaces of fractional integrals on a rectilinear contour,” Izv. Akad. Nauk ArmSSR, Ser. Matem.,7, No. 5, 373–386 (1972).

    Google Scholar 

  32. L. Hörmander, Estimates for Operators Invariant under a Shift [Russian translation], IL, Moscow (1962).

    Google Scholar 

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Authors
  1. N. K. Karapetyants
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  2. S. G. Samko
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Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 16, No. 1, pp. 44–61, Junuary–February, 1975.

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Karapetyants, N.K., Samko, S.G. Singular convolution operators with a discontinuous symbol. Sib Math J 16, 35–48 (1975). https://doi.org/10.1007/BF00967460

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