arXiv subjects
Publications and source records attributed to G. Tephnadze.
The main aim of this note is to derive necessary and sufficient conditions for the convergence of Fejér means in terms of the modulus of continuity of the Hardy spaces $H_{p},$ $\left(0<p\leq 1\right)$.
In this paper we prove and discuss some new $\left(H_{p},weak-L_{p}\right) $ type inequalities of maximal operators of Vilenkin-Nörlund means with monotone coefficients. We also apply these results to prove a.e. convergence of such Vilenkin-Nörlund means. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out.
In this paper we derive the maximal subspace of positive numbers, for which the restricted maximal operator of Fejér means in this subspace is bounded from the Hardy space $H_{p}$ to the space $L_{p}$ for all $0<p\leq 1/2.$ Moreover, we prove that the result is in a sense sharp.