arXiv subjects
Publications and source records attributed to George Tephnadze.
The main aim of this paper is to investigate Paley type and Hardy-Littlewood type inequalities and strong convergence theorem of partial sums of Vilenkin-Fourier series.
The main aim of this paper is to prove that the maximal operator $\overset{% \sim }{σ}^{*}f:=\underset{n\in P}{\sup }\frac{\left| σ_{n}f\right| }{\log ^{2}\left( n+1\right) }$ is bounded from the Hardy space $H_{1/2}$ to the space $L_{1/2}$, where $σ_{n}f$ is Fejér means of bounded Vilenkin-Fourier series.
The main aim of this paper is to prove that when $0<p<1/2$ the maximal operator $\overset{\sim }{σ}_{p}^{\ast }f:=\underset{n\in \mathbb{N}}{% \sup }\frac{\left\vert σ_{n}f\right\vert }{\left( n+1\right) ^{1/p-2}}$ is bounded from the martingale Hardy space $H_{p}$ to the space $L_{p},$ where $σ_{n}$ is $n$-th Fejér mean with respect to bounded Vilenkin system.
We prove that certain mean of the quadratical partial sums of the two-dimensional Walsh-Fourier series are uniformly bounded operators from the Hardy space $H_{p}$ to the space $L_{p}$ for $0<p<1.$
The main aim of this paper is to investigate the quadratical partial sums of the two-dimensional Walsh-Fourier series.
The main aim of this paper is to investigate weighted maximal operators of partial sums of Vilenkin-Fourier series. We also use our results to prove approximation and strong convergence theorems on the martingale Hardy spaces $H_{p},$ when $0<p\leq 1.$
The main aim of this paper is to investigate $\left( H_{p},L_{p}\right) $ and $\left( H_{p},L_{p,\infty }\right) $ type inequalities for maximal operators of Riesz logarithmic means of one-dimensional Vilenkin-Fourier series.
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 spaces $H_{p},$ when $0<p\leq 1/2.$
As main result we prove that Fejér means of Walsh-Fourier series are uniformly bounded operators from $\ H_{p}$ to $H_{p}$ $\left( 0<p\leq 1/2\right) .
The main aim of this paper is to prove that the maximal operator $σ_{p}^{κ,\ast }f:=\sup_{n\in \mathbf{P}}\left\vert σ_{n}^{κ}f\right\vert /\left( n+1\right) ^{1/p-2}$ is bounded from the Hardy space $% H_{p}$ to the space $L_{p},$ for $0<p<1/2$.
The main aim of this paper is to find the estimation for Vilenkin-Fourier coefficients.
TThe main aim of this paper is to prove that there exist a martingale $f\in H_{1/2}$ such that Fejér means of Vilenkin-Fourier series of the martingale $f$ is not uniformly bounded in the space $L_{1/2}.$
The main aim of this paper is to find the necessary and sufficient conditions for a modulus of continuity of a martingale $F\in H_{p},$ for which Fejér means convergence in $H_{p}$-norm, when $0<p\leq 1/2.$
We prove inclusion relations between generalized Waterman's and generalized Wiener's classes for functions of two variable.