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Generalized Absolute Convergence of Series of Fourier Coefficients With Respect to Haar Type Systems

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Abstract

For the orthogonal systems ofHaar type, introduced by Vilenkin in 1958, we study absolute convergence of series composed from positive powers of Fourier coefficients with multiplicators from the Gogoladze–Meskhia class. The conditions for convergence of the series are given in terms of either best approximations of functions in Lp spaces by polynomials with respect to Haar type systems or fractional modulus of continuity for functions from the Wiener spaces V p , p > 1. We establish the sharpness of the obtained results.

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Authors and Affiliations

  1. Saratov State University, ul. Astrakhanskya 83, Saratov, 410012, Russia

    S. S. Volosivets

  2. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow Region, 141700, Russia

    B. I. Golubov

Authors
  1. S. S. Volosivets
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  2. B. I. Golubov
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Correspondence to S. S. Volosivets.

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Original Russian Text © S.S. Volosivets, B.I. Golubov, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 1, pp. 10–20.

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Volosivets, S.S., Golubov, B.I. Generalized Absolute Convergence of Series of Fourier Coefficients With Respect to Haar Type Systems. Russ Math. 62, 7–16 (2018). https://doi.org/10.3103/S1066369X18010024

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  • DOI: https://doi.org/10.3103/S1066369X18010024

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