A weak type inequality for the two-dimensional diagonal Sunouchi operator on the Hardy space

Define the two dimensional diagonal Sunouchi operator where S 2 n , 2 n ƒ and σ 2 n ƒ are the (2 n , 2 n )th cubic-partial sums and 2 n th Marcinkiewicz–Fejér means of a two-dimensional Walsh–Fourier series. The main aim of this paper is to prove that the operator is bounded from the Hardy space H 1/2 to the weak L 1/2 space and is not bounded from the Hardy space H 1/2 to the space L 1/2.