Affiliation:
1. I. Javakhishvili Tbilisi State University, Chavchavadze St. 1, Tbilisi 0128, Georgia.
Abstract
Abstract
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.