Abstract. Our goal is to show that the dyadic Cesàro operator is bounded on $L^p[0,1)$ $(1\le p< \infty )$ and on the dyadic Hardy space $H^1[0,1)$ and isn't bounded on the spaces VMO and on $L^\infty[0,1)$. Due to the duality we can easily discuss the boundedness of the Copson operator, which is the adjoint operator of the Cesàro operator. The boundedness of the Cesàro operator on $L^p$ $(1\le p< \infty )$ and on the Hardy space has been already examined for the trigonometric system (see [6] and [3]).

AMS Subject Classification (1991): 42C10, 42B30

Received May 20, 1997 and in revised form September 23, 1997. (Registered under 2656/2009.)