arXiv subjects
Publications and source records attributed to L. E. Persson.
In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin-Fourier (Walsh-Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp, at least for the case with Walsh-Fourier series.
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.
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.
In this paper we prove and discuss some new $\left(H_{p},L_{p}\right)$ type inequalities of maximal operators of Vilenkin-Nörlund means with non-decreasing coefficients. We also apply these inequalities to prove strong convergence theorems of such Vilenkin-Nörlund means. These inequalities are the best possible in a special sense. As applications, both some well-known and new results are pointed out.
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.