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Multipliers of Absolute Convergence

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Abstract

The paper deals with sequences of positive numbers (dn) such that, multiplying the Fourier coefficients (Cn(f)) of functions from given function classes by these numbers, one obtains a convergent series of the form \(\sum {{\rm{|}}{C_n}(f){{\rm{|}}^p}{d_n}, 1 \le p < 2} \). It is established that the resulting conditions cannot be strengthened in a certain sense. The results of the paper imply, in particular, some well-known results for trigonometric Fourier series.

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References

  1. G. Hardy, J. E. Littlewood, and G. Pólya, Inequalities (Cambridge Univ. Press, Cambridge, 1934; Inostr. Lit., Moscow, 1948).

    MATH  Google Scholar 

  2. V. Sh. Tsagareishvili, “Absolute convergence of Fourier series of functions of class Lip 1 and of functions of bounded variation,” Izv. Ross. Akad. Nauk Ser. Mat. 76 (2), 215–224 (2012) [Izv. Math. 76 (2), 419–429 (2012)].

    Article  MathSciNet  MATH  Google Scholar 

  3. A. M. Olevskii, “Orthogonal series in terms of complete systems,” Mat. Sb. 58 (100) (2), 707–748 (1962).

    MathSciNet  Google Scholar 

  4. B. C. Kashin and A. A. Saakyan, Orthogonal Series (Izd. AFTs, Moscow, 1999) [in Russian].

    MATH  Google Scholar 

  5. G. Aleksich, Problems of Convergence of Orthogonal Series (Inostr. Lit., Moscow, 1963) [in Russian].

    Google Scholar 

  6. “On Fourier series of continuous functions with respect to a Haar system,” Izv. Akad. Nauk SSSR Ser. Mat. 28 (6), 1271–1296 (1964).

  7. H. K. Bari, Trigonometric Series (Fizmatgiz, Moscow, 1961) [in Russian].

    Google Scholar 

  8. J. R. McLaughlin, “Integrated orthonormal series,” Pacific J. Math. 42, 469–475 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  9. S. V. Bochkarev, “On the absolute convergence of Fourier series in bounded complete orthonormal systems of functions,” Mat. Sb. 93 (135) (2), 203–217 (1974) [Math. USSR-Sb. 22 (1), 201–216 (1974)].

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Tbilisi State University, Tbilisi, 380028, Georgia

    V. Sh. Tsagareishvili & G. Tutberidze

Authors
  1. V. Sh. Tsagareishvili
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  2. G. Tutberidze
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Correspondence to V. Sh. Tsagareishvili or G. Tutberidze.

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Tsagareishvili, V.S., Tutberidze, G. Multipliers of Absolute Convergence. Math Notes 105, 439–448 (2019). https://doi.org/10.1134/S0001434619030143

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  • DOI: https://doi.org/10.1134/S0001434619030143

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