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On absolute convergence of multiple Fourier series

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Abstract

We consider absolute convergence of multiple series of Fourier-Haar coefficients for functions of many variables with partial derivatives of higher order. We show that the obtained results are best possible for general orthonormal systems.

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References

  1. Kashin, B. S., Saakyan, A. A. Orthogonal Series (AFS, Moscow, 1999) [in Russian].

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  4. Gogoladze, L. D., Tsagareishvili, V. Sh. “The Absolute Convergence of the Fourier-Haar Series for Two-Dimensional Functions,” Russian Mathematics (Iz. VUZ) 52, No.5, 9–19 (2008).

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Authors and Affiliations

  1. Tbilisi State University, pr. I. Chavchavadze 1, Tbilisi, 0128, Republic of Georgia

    L. D. Gogoladze & V. Sh. Tsagareishvili

Authors
  1. L. D. Gogoladze
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  2. V. Sh. Tsagareishvili
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Corresponding author

Correspondence to L. D. Gogoladze.

Additional information

Original Russian Text © L.D. Gogoladze, V.Sh. Tsagareishvili, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 9, pp. 12–21.

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Gogoladze, L.D., Tsagareishvili, V.S. On absolute convergence of multiple Fourier series. Russ Math. 59, 9–17 (2015). https://doi.org/10.3103/S1066369X15090029

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  • DOI: https://doi.org/10.3103/S1066369X15090029

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