On the Boundedness of Dyadic Hardy and Hardy-Littlewood Operators on the Dyadic Spaces H and BMO

Dyadic analogs of the integral Hardy and Hardy-Littlewood operators on R ₊ are introduced. It is proved that the first of them is bounded on the dyadic Hardy space H _d (R ₊), while the second one is bounded on the dyadic space BMO _d (R ₊) of functions of bounded mean oscillation on R ₊.