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Norm convergence of double Fourier series on unbounded Vilenkin groups

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Abstract

We study approximation by rectangular partial sums of double Fourier series on unbounded Vilenkin groups in the spaces C and L 1. From these results we obtain criterions of the uniform convergence and L-convergence of double Vilenkin–Fourier series. We also prove that these results are sharp.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, H-4002, Debrecen, Pf. 400, Hungary

    G. Gát

  2. Department of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze str. 1, Tbilisi, 0128, Georgia

    U. Goginava

Authors
  1. G. Gát
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  2. U. Goginava
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Correspondence to G. Gát.

Additional information

The first author was supported by the Hungarian National Foundation for Scientific Research (OTKA), grant no. K111651.

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Gát, G., Goginava, U. Norm convergence of double Fourier series on unbounded Vilenkin groups. Acta Math. Hungar. 152, 201–216 (2017). https://doi.org/10.1007/s10474-017-0703-9

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  • DOI: https://doi.org/10.1007/s10474-017-0703-9

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