O the absolute Nörlund summability of a series associated with a Fourier series.
In this paper a theorem on summability factors, which generalizes a theorem of Mishra and Srivastava [MS] on summability factors, has been proved.
Let G be the Walsh group. For we prove the a. e. convergence σf → f(n → ∞), where is the nth (C,1) mean of f with respect to the Walsh-Kaczmarz system. Define the maximal operator We prove that σ* is of type (p,p) for all 1 < p ≤ ∞ and of weak type (1,1). Moreover, , where H is the Hardy space on the Walsh group.