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Tohoku Mathematical Journal
SECOND SERIES VOL. 64, NO. 3
|Tohoku Math. J.|
64 (2012), 317-331
APPROXIMATION BY CESÀRO MEANS OF NEGATIVE ORDER OF DOUBLE WALSH-KACZMARZ-FOURIER SERIES
(Received July 28, 2010)
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.
Key words and phrases.
Walsh group, Walsh-Kaczmarz system, double Walsh-Kaczmarz-Fourier series, Cesàro means, rate of convergence, approximation.
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