Tohoku Mathematical Journal
2012
September
SECOND SERIES VOL. 64, NO. 3

Tohoku Math. J.
64 (2012), 317-331

Title APPROXIMATION BY CESÀRO MEANS OF NEGATIVE ORDER OF DOUBLE WALSH-KACZMARZ-FOURIER SERIES

Author Károly Nagy

(Received July 28, 2010)
Abstract. In this article we investigate the rate of the approximation by Cesàro means of the quadratical partial sums of double Walsh-Kaczmarz-Fourier series of a function in the Lebesgue space over the Walsh group. The approximation properties of Cesàro means of negative order of one- and two-dimensional Walsh-Fourier series was discussed earlier by Goginava.

2000 Mathematics Subject Classification. Primary 42C10.
Key words and phrases. Walsh group, Walsh-Kaczmarz system, double Walsh-Kaczmarz-Fourier series, Cesàro means, rate of convergence, approximation.

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