Related papers: On the strong convergence of partial sums with res…
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
In this paper we discuss and prove some new strong convergence theorems for partial sums and Fej\'er means with respect to the Vilenkin system.
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…
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.
As main result we prove strong convergence theorems of Vilenkin-Fej\'er means when $0<p\leq 1/2.$
This paper deals with strong invariance principles (known also as strong approximation theorems) for sums of the form $\sum_{n=1}^{[Nt]}F\big(X(n),X(2n),...,X(kn), X(q_{k+1}(n)),X(q_{k+2}(n)),..., X(q_\ell(n))\big)$
In this paper we investigate convergence and strong summability of the two-dimensional Vilenkin-Fourier series in the martingale Hardy spaces.
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…
We prove a convergence theorem for partial sums of sectorial forms with vertex zero and a common semi-angle. As an example we prove an absorption theorem for sectorial forms.
In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…
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…
The main aim of this paper is to investigate the quadratical partial sums of the two-dimensional Walsh-Fourier series.
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…
We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…
This article establishes a real-variable argument for Zygmund's theorem on almost everywhere convergence of strong arithmetic means of partial sums of Fourier series on $\mathbb{T}$, up to passing to a subsequence. Our approach extends to,…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem…
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 these results we obtain relationship of the ratio of…
In this paper we derive converge of $T$ means of Vilenkin-Fourier series with monotone coefficients of integrable functions in Lebesgue and Vilinkin-Lebesgue points. Moreover, we discuss pointwise and norm convergence in $L_p$ norms of such…
In the present paper, a generalization of the first part of the Borel-Cantelli lemma is obtained by the recent work of Balakrishnan and Stepanov (2010). This generalization is further applied to derive strong limit results for the sequence…