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Abstract. In this paper we discuss some convergence and divergence properties of subsequences of partial sums and logarithmic means of Walsh--Fourier series of functions in the uniform, and in the $L$ Lebesgue norm. We give necessary and sufficient conditions for the convergence regarding the modulus of continuity of the function. It is also proved that there exists a bounded function for which the logarithmic means converge and the partial sums diverge.
AMS Subject Classification
(1991): 42C10
Keyword(s):
Walsh--Fourier series,
Norm convergence,
Logarithmic means
Received January 17, 2005, and in revised form April 6, 2005. (Registered under 5916/2009.)
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