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BMO-Estimation and Almost Everywhere Exponential Summability of Quadratic Partial Sums of Double Fourier Series

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Abstract

A \(\mathrm{BMO\,}\)-estimation for quadratic partial sums of two-dimensional Fourier series is proved from which is derived an almost everywhere exponential summability of quadratic partial sums of double Fourier series.

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Acknowledgments

The authors would like to thank the referees for helpful suggestions. The research of U. Goginava was supported by Shota Rustaveli National Science Foundation Grant No. 31/48 (Operators in some function spaces and their applications in Fourier analysis).

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Authors and Affiliations

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

    U. Goginava & L. Gogoladze

  2. Institue of Mathematics of Armenian National Academy of Science, Bughramian Ave. 24/5, 375019 , Yerevan, Armenia

    G. Karagulyan

Authors
  1. U. Goginava
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  2. L. Gogoladze
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  3. G. Karagulyan
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Correspondence to U. Goginava.

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Communicated by Vilmos Totik.

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Goginava, U., Gogoladze, L. & Karagulyan, G. BMO-Estimation and Almost Everywhere Exponential Summability of Quadratic Partial Sums of Double Fourier Series. Constr Approx 40, 105–120 (2014). https://doi.org/10.1007/s00365-014-9234-6

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  • DOI: https://doi.org/10.1007/s00365-014-9234-6

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