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Properties of Sums of Double Trigonometric Series with Multiply Monotone Coefficients

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Abstract

Sums of double sine and cosine series with multiply monotone coefficients are studied. Sufficient conditions for such sums to belong to Orlich’s weighted classes are obtained.

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REFERENCES

  1. E. T. Whitteker and G. N. Watson, A Course of Modern Analysis (Cambridge Univ. Press, Cambridge, 1927; Fizmatgiz, Moscow, 1962).

  2. T. M. Vukolova and M. I. D’yachenko, ‘‘Bounds for mixed norms of sums of double trigonometrical series with multiply monotone coefficients,’’ Russ. Math. 41 (7), 1–11 (1997).

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  4. B. V. Simonov, ‘‘Sine and cosine series in \(L_{\varphi}\) classes,’’ Russ. Math. 57, 19–36 (2013). doi 10.3103/S1066369X13100034

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Authors and Affiliations

  1. Institute of Russian Language and Culture, Moscow State University, 117218, Moscow, Russia

    T. M. Vukolova

  2. Volgograd State Technical University, 400005, Volgograd, Russia

    B. V. Simonov

Authors
  1. T. M. Vukolova
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  2. B. V. Simonov
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Corresponding authors

Correspondence to T. M. Vukolova or B. V. Simonov.

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The authors declare that they have no conflicts of interest.

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Vukolova, T.M., Simonov, B.V. Properties of Sums of Double Trigonometric Series with Multiply Monotone Coefficients. Moscow Univ. Math. Bull. 75, 188–203 (2020). https://doi.org/10.3103/S0027132220050083

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  • DOI: https://doi.org/10.3103/S0027132220050083

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