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Sharp inequalities for the norms of conjugate functions and their applications

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Literature cited

  1. N. K. Bari (N. K. Bary), A Treatise on Trigonometrie Series, I and II, Macmillan, New York (1964).

    Google Scholar 

  2. N. P. Korneichuk, Extremal Problems of Approximation Theory [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  3. N. P. Korneichuk, A. A. Ligun, and V. G. Doronin, Approximation with Constraints [in Russian], Naukova Dumka, Kiev (1976).

    Google Scholar 

  4. N. P. Korneichuk, Splines in Approximation Theory [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  5. N. I. Akhiezer (N. Achyeser) and M. G. Krein (M. Krein), Sur la meilleure approximation des fonctions périodiques dérivables au moyen de sommes trigonométriques,” Dokl. Akad. Nauk SSSR,15, No. 3, 107–111 (1937).

    Google Scholar 

  6. S. M. Nikol'skii, “Approximation of functions in the mean by trigonometric polynomials,” Izv. Akad. Nauk SSSR, Ser. Mat.,10, 207–256 (1946).

    Google Scholar 

  7. V. F. Babenko, “Inequalities for rearrangements of differentiable periodic functions, approximation problems, and approximate integration,” Dokl. Akad. Nauk SSSR,272, No. 5, 1038–1041 (1983).

    Google Scholar 

  8. E. M. Stein and G. Weiss, “An extension of a theorem of Marcinkiewicz and some of its applications,” J. Math. Mech.,8, No. 2, 263–284 (1959).

    Google Scholar 

  9. B. V. Khvedelidze, “The method of Cauchy type integrals in discontinuous boundary value problems of the theory of holomorphic functions of a complex variable,” Sov. Probl. Mat.,7, 5–162 (1975).

    Google Scholar 

  10. L. Hörmander, “A new proof and a generalization of an inequality of Bohr,” Math. Scand.,2, 33–45 (1954).

    Google Scholar 

  11. V. F. Babenko, “Nonsymmetric extremal problems of approximation theory,” Dokl. Akad. Nauk SSSR,269, No. 3, 521–524 (1983).

    Google Scholar 

  12. V. G. Doronin and A. A. Ligun, “Best one-sided approximation of some classes of functions,” Mat. Zametki,29, No. 3, 431–454 (1981).

    Google Scholar 

  13. A. Zygmund, Trigonometric Series, Vols. I and II, Cambridge Univ. Pres (1959).

  14. L. V. Taikov, “A generalization of an inequality of S. N. Bernshtein,” Trudy Mat. Inst. Akad. Nauk SSSR,78, 43–47 (1965).

    Google Scholar 

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Authors and Affiliations

  1. Dnepropetrovsk University, USSR

    V. F. Babenko

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  1. V. F. Babenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 39, No. 2, pp. 139–144, March–April, 1987.

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Babenko, V.F. Sharp inequalities for the norms of conjugate functions and their applications. Ukr Math J 39, 115–119 (1987). https://doi.org/10.1007/BF01057488

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  • DOI: https://doi.org/10.1007/BF01057488

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