35 citations · 137 across the 36 of their papers we have counts for
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Some new restricted maximal operators of Fejér means of Walsh-Fourier series in the space
Davit Baramidze, Lars-Erik Persson, George Tephnadze
In this paper we derive the maximal subspace of natural numbers , such that the restricted maximal operator, defined by $\sup_{k\in \mathbb{N}}\left\v…
Weighted maximal operators of Fejér means of Walsh-Fourier series in the martingale Hardy space
Nika Areshidze, Davit Baramidze, Lars-Erik Persson +1
In this paper we derive the restricted weighted maximal operator, defined by of Fejér means of Walsh-Four…
Sharpness of some Hardy-type inequalities
Lars-Erik Persson, Natasha Samko, George Tephnadze
The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the L…
Almost everywhere and norm convergence of Approximate Identity and Fejér means of trigonometric and Vilenkin systems
N. Nadirashvili, G. Tephnadze, G. Tutberidze
In this paper, we investigate very general approximation kernels with special properties, called an approximate identity, and prove almost everywhere and norm convergence of these…
Some new results for subsequences of Nörlund logarithmic means of Walsh-Fourier series
D. Baramidze, L. -E. Persson, H. Singh +1
We prove that there exists a martingale such that the subsequence of Nörlund logarithmic means with respect to the Walsh system are not bounded in the L…
Strong convergence theorem for Walsh-Kaczmarz-Fejér means
Nata Gogolashvili, Károly Nagy, George Tephnadze
As main result we prove that Fejér means of Walsh-Kaczmarz-Fourier series are uniformly bounded operators from the Hardy martingale space to the Hardy martingale space $H…
The One-dimensional Martingale Hardy Spaces and Partial Sums and Fejér Means with respect to Walsh system
George Tephnadze
In this paper we prove and discuss some new type inequalities for partial Sums and Fejér means with respect to Walsh system. It is also proved that these…
Convergence and Strong Summability of the Two-dimensional Vilenkin-Fourier Series
G. Tephnadze
In this paper we investigate convergence and strong summability of the two-dimensional Vilenkin-Fourier series in the martingale Hardy spaces.
A note on strong summability of two-dimensional Walsh-Fourier series
George Tephnadze
In this paper we investigate strong summability of the two-dimensional Walsh-Fourier series obtained in Weisz \cite{We} (see Theorem W) and prove sharpness of this result.
Some new resuts on strong convergence of Fejér means with respect to Vilenkin systems
L-E. Persson, G. Tephnadze, G. Tutberidze
In this paper we discuss and prove some new strong convergence theorems for partial sums and Fejér means with respect to the Vilenkin system.
On the Partial Sums and Marcinkiewicz and Fejér Means on the One- and Two-dimensional One-parameter Martingale Hardy Spaces
George Tephnadze
In this PhD thesis we are dealing with convergence and summability of partial sums, Fejér and Marcinkiewicz means with respect to one- and two-dimensional Walsh-Fourier series on t…
A note on The maximal operators of the Nörlund logaritmic means of Vilenkin-Fourier series
George Tephnadze, Giorgi Tutberidze
The main aim of this paper is to investigate - type inequalities for the the maximal operators of Nörlund logaritmic means, for
Ph.D. Thesis-Martingale Hardy spaces and summability of the one dimensional Vilenkin-Fourier series
George Tephnadze
In this PhD thesis we discuss, develop and apply this fascinating theory connected to modern harmonic analysis. In particular we make new estimations of Vilenkin-Fourier coefficien…
A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces
I. Blahota, K. Nagy, L. E. Persson +1
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 opera…
On the convergence of partial sums with respect to Vilenkin system on the martingale Hardy spaces
G. Tephnadze
In this paper we derive characterizations of boundedness of the subsequences of partial sums with respect to Vilenkin system on the martingale Hardy spaces when . Moreover…
Strong convergence of two--dimensional Vilenkin-Fourier series
N. Memiæ, I. Simon, G. Tephnadze
We prove that certain means of the quadratical partial sums of the two-dimensional Vilenkin-Fourier series are uniformly bounded operators from the Hardy space to the space…
On the partial sums of Walsh-Fourier series
George Tephnadze
In this paper we investigate some convergence and divergence of some specific subsequences of partial sums with respect to Walsh system on the martingale Hardy spaces. By using the…
Strong convergence theorem of Cesàro means with respect to the Walsh system
István Blahota, George Tephnadze, Rodolfo Toledo
We prove that Cesàro means of one-dimensional Walsh-Fourier series are uniformly bounded operators in the martingale Hardy space for
Some new type inequalities of maximal operators of Vilenkin-Nörlund means with non-decreasing coefficients
L. E. Persson, G. Tephnadze, P. Wall
In this paper we prove and discuss some new type inequalities of maximal operators of Vilenkin-Nörlund means with non-decreasing coefficients. We also ap…
On the -means with respect to the Walsh system
I. Blahota, G. Tephnadze
As main result we prove strong convergence theorems for Cesáro means on the Hardy spaces % , where
Maximal operators of Vilenkin-Nörlund means
L. E. Persson, G. Tephnadze, P. Wall
In this paper we prove and discuss some new type inequalities of maximal operators of Vilenkin-Nörlund means with monotone coefficients. We also ap…
A note on the norm convergence by Vilenkin-Fejér means
George Tephnadze
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Fejér means in terms of the modulus of continuity on the Hardy spaces when…
A sharp boundedness result concerning some maximal operators of Vilenkin-Fejér means
L. E. Persson, G. Tephnadze
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 …
Approximation by Walsh-Kaczmarz-Fejér means on the Hardy space
George Tephnadze
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fejér means in the terms of the modulus of continuity on the Hardy s…