Two-parameter Vilenkin multipliers and a square function (Q1416117)

The author investigates the two-parameter Vilenkin systems. He gives a general sufficient condition for multipliers to be bounded between two-dimensional Hardy spaces \(H^q\) (\(0<q\leq 1\)). By means of interpolation and duality argument, his theorem can be extended to other spaces. As a consequence he can prove the \((H^q, L^q)\)-boundedness of the Sunouchi operator \(U\) with respect to two-parameter Vilenkin systems for all \(0<q\leq 1\). Moreover, the equivalence \(\|f\|_{H^q}\sim \|Uf\|_{q}\) (\(f\in H^q\)) follows for \(1/2 < q\leq 1\).