Abstract. It is well known that the Walsh functions form an orthonormal system on the unit interval. The weighted Walsh functions are also orthonormal with respect to some weight function. The almost everywhere convergence of the $(C,1)$ means of Walsh--Fourier series of integrable functions is an old result of Fine [fine]. The main aim of this paper is to generalize this a.e. convergence relation with respect to weighted Walsh systems.

DOI: 10.14232/actasm-015-024-5

AMS Subject Classification (1991): 42C10

Keyword(s): weighted Walsh system, Fejér means, almost everywhere convergence

Received March 24, 2015. (Registered under 24/2015.)