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Strong approximation by Marcinkiewicz means of two-dimensional Walsh–Kaczmarz–Fourier series

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In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the best possible.

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Authors and Affiliations

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

    U. Goginava

  2. Institute of Mathematics and Computer Sciences, University of Nyíregyháza, Sóstói str. 31/B, 4400, Nyíregyháza, Hungary

    K. Nagy

Authors
  1. U. Goginava
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  2. K. Nagy
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Correspondence to K. Nagy.

Additional information

The research of first author was supported by Shota Rustaveli National Science Foundation grant no. DI/9/5-100/13 (Function spaces, weighted inequalities for integral operators and problems of summability of Fourier series).

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Goginava, U., Nagy, K. Strong approximation by Marcinkiewicz means of two-dimensional Walsh–Kaczmarz–Fourier series. Anal Math 42, 143–157 (2016). https://doi.org/10.1007/s10476-016-0203-0

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  • DOI: https://doi.org/10.1007/s10476-016-0203-0

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