arXiv subjects
Publications and source records attributed to I. Blahota.
The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space $%H_{p}$ to the Lebesgue space $L_{p}$ for all $0<p\leq 1.$ We also prove that the result is sharp in a particular sense.
As main result we prove strong convergence theorems for Cesáro means $% \left(C,α\right) $ on the Hardy spaces $H_{1/\left(1+α\right) } $% , where $0<α<1.$
In this paper we prove and discuss some new $\left( H_{p},L_{p}\right)$-type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients. These results are the best possible in a special sense. As applications, both some well-known and new results are pointed out in the theory of strong convergence of Vilenkin-Nörlund means with non-increasing coefficients.
As main result we prove strong convergence theorems of Vilenkin-Fejér means when $0<p\leq 1/2.$