Abstract. In 1992, Móricz and Siddiqi [4] studied the approximation properties of Walsh--Nörlund means in $L^p$ spaces. This study embraced earlier results in this area by Yano, Jastrebova, and Skvorcov on the rate of approximation by Cesáro means. The main objective of this paper is to improve, and to extend the results of Móricz and Siddiqi [MS] to dyadic homogeneous Banach spaces, and to dyadic Hardy spaces $H^p$, $p<1$.

AMS Subject Classification (1991): 42C10, 41A25, 41A65, 60G42

Keyword(s): Walsh system, Nörlund means, Homogeneous Banach spaces, Hardy spaces

Received July 10, 2008, and in revised form August 27, 2008. (Registered under 6034/2009.)