On the Approximation Properties of Cesàro Means of Negative Order of Walsh–Fourier Series

Author： Goginava U.  

Publisher： Academic Press

ISSN： 0021-9045

Source： Journal of Approximation Theory, Vol.115, Iss.1, 2002-03, pp. : 9-20

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Abstract

In this paper we establish approximation properties of Cesàro (C, -α)-means with α∈(0, 1) of Walsh–Fourier series. This result allows one to obtain the condition which is sufficient for the convergence of the means σ-αn(f, x) to f(x) in the Lp-metric. We also show that this condition cannot be improved in the case p=1. © 2002 Elsevier Science (USA).

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