Abstract
We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m;k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fej er means of the Ciesielski{Fourier series is bounded from the Hardy space Hp to Lp if 1=2 < p <1 and m 0,jkj m + 1. Moreover, it is of weak type (1; 1). As a consequence, the Fej er means of the Ciesielski{Fourier series of a function f converges to f a.e. if f2 L1 as n!1.
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