Related papers: On the partial sums of Walsh-Fourier series
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 $ 0<p<1 $. Moreover, we find necessary and sufficient conditions for the…
In this PhD thesis we are dealing with convergence and summability of partial sums, Fej\'er and Marcinkiewicz means with respect to one- and two-dimensional Walsh-Fourier series on the martingale Hardy spaces. This thesis is focus to…
The main aim of this paper is to investigate the quadratical partial sums of the two-dimensional Walsh-Fourier series.
In this paper we prove and discuss some new $\left( H_p,L_{p}\right)$ type inequalities for partial Sums and Fej\'er means with respect to Walsh system. It is also proved that these results are the best possible in a special sense. As…
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…
The aim of my thesis is to discuss, develop and apply the newest developments of this fascinating theory connected to modern harmonic analysis. In particular, we investigate some strong convergence result of partial sums of Vilenkin-Fourier…
In this paper we discuss some convergence and divergence properties of subsequences of logarithmic means of Walsh-Fourier series . We give necessary and sufficient conditions for the convergence regarding logarithmic variation of numbers.
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 Fej\'er means convergence in $H_{p}$-norm, when $0<p\leq 1/2.$
The convergence of partial sums and Ces\'aro means of negative order of double Walsh-Fourier series of functions of bounded \ generalized variation is investigated.
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 coefficients and prove some new results concerning boundedness of…
In this paper we investigate convergence and strong summability of the two-dimensional Vilenkin-Fourier series in the martingale Hardy spaces.
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 $0<p<1.$
In the first part of this paper we describe the status of the art of this subject. In the second part we present and motivate some new results. Indeed, we introduce some new weighted maximal operators of the partial sums of the…
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej\'er means in the terms of the modulus of continuity on the Hardy spaces $H_{p},$ when $0<p\leq 1/2.$
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.
In this paper, we consider norm convergence for a special matrix-based de la Vall\'ee Poussin-like mean of Fourier series for the Walsh system. We estimate the difference between the named mean above and the corresponding function in norm,…
We investigate the subsequence $\{t_{2^n}f \}$ of N\"{o}rlund means with respect to the Walsh system generated by non-increasing and convex sequences. In particular, we prove that a big class of such summability methods are not bounded from…
In this paper, we investigate the convergence properties of Fourier partial sums associated with general orthonormal systems, focusing on functions that belong to specific differentiable function classes. While classical Fourier analysis…
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
We prove that Ces\`{a}ro means of one-dimensional Walsh-Fourier series are uniformly bounded operators in the martingale Hardy space $H_{p}$ for $% 0<p<1/\left( 1+\alpha \right).$