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Majorant operators of strong summation of Fourier series

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Abstract

Inequalities of weak type (1, 1) are established for the operators that are majorant for strong means of the Fourier series in the trigonometric and the Walsh systems.

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Literature cited

  1. 1.

    A. Zygmund, Trigonometric Series, Vols. 1 and 2, Cambridge Univ. Press, Cambridge (1959).

  2. 2.

    B. S. Kashin and A. A. Saakyan, Orthogonal Series [in Russian], Nauka, Moscow (1984).

  3. 3.

    V. A. Rodin, Application of the Space BMO for the Study of the E-Strong Means of the Fourier Series in the Trigonometric System [in Russian], Voronezh (1988), Deposited in the All-union Institute for Scientific and Technical Information at No. 1320–V 88.

  4. 4.

    E. M. Stein, “On limits of sequences of operators,” Ann. Math.,74, No. 1, 140–170 (1961).

  5. 5.

    J. Garnett, Bounded Analytic Functions, Academic Press, London and New York (1981).

  6. 6.

    B. I. Golubov, A. V. Efimov, and V. A. Skvortsov, Walsh Series and Transforms [in Russian], Nauka, Moscow (1987).

  7. 7.

    V. A. Rodin, The Space BMO and Strong Means of the Fourier—Wash Series [in Russian], Voronezh (1988), Deposited in the All-Union Institute of Scientific and Technical Information at No. 1319–V887.

  8. 8.

    K. I. Oskolkov, “On the strong summability of Fourier series,” Tr. Mat. Inst. Akad. Nauk SSSR,172, 280–290 (1985).

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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 710–713, May, 1990.

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Rodin, V.A. Majorant operators of strong summation of Fourier series. Ukr Math J 42, 628–630 (1990). https://doi.org/10.1007/BF01065072

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Keywords

  • Fourier Series
  • Weak Type
  • Majorant Operator
  • Walsh System
  • Strong Summation