Corpus ID: 235731842

Lebesgue and Vilenkin-Lebesgue points and a.e. Convergence of T means with respect to Vilenkin systems of integrable functions

@inproceedings{Baramidze2021LebesgueAV,
  title={Lebesgue and Vilenkin-Lebesgue points and a.e. Convergence of T means with respect to Vilenkin systems of integrable functions},
  author={Davit Baramidze and N. G. Gogolashvili and N. R. Nadirashvili},
  year={2021}
}
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 Lp norms of such T means. 2000 Mathematics Subject Classification. 42C10, 42B25. 

References

SHOWING 1-10 OF 57 REFERENCES
TWO-SIDED ESTIMATES OF THE LEBESGUE CONSTANTS WITH RESPECT TO VILENKIN SYSTEMS AND APPLICATIONS
Abstract In this paper, we derive two-sided estimates of the Lebesgue constants for bounded Vilenkin systems, we also present some applications of importance, e.g., we obtain a characterization forExpand
On the boundedness of subsequences of Vilenkin-Fejér means on the martingale Hardy spaces
In this paper we characterize subsequences of Fejer means with respect to Vilenkin systems, which are bounded from the Hardy space $H_{p}$ to the Lebesgue space $L_{p},$ for all $0<p<1/2.$ The resultExpand
Fejér means of Vilenkin-Fourier series
The main aim of this paper is to prove that there exist a martingale f ∈ H1/2 such that Fejer means of Vilenkin-Fourier series of the martingale f is not uniformly bounded in the space L1/2.
A Sharp Boundedness Result Concerning Some Maximal Operators of Vilenkin–Fejér Means
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 Hp to the space Lp for allExpand
Maximal Operators of Vilenkin–Nörlund Means
In this paper we prove and discuss some new $$\left( H_{p},weak-L_{p}\right) $$Hp,weak-Lp type inequalities of maximal operators of Vilenkin–Nörlund means with monotone coefficients. We also applyExpand
On the partial sums of Vilenkin-Fourier series
The aim of this paper is to investigate weighted maximal operators of partial sums of Vilenkin-Fourier series. Also, the obtained results we use to prove approximation and strong convergence theoremsExpand
On the Nörlund means of Vilenkin-Fourier series
We prove and discuss some new (Hp,Lp)-type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients {qk: k ⩾ 0}. These results are the best possible in aExpand
Some inequalities related to strong convergence of Riesz logarithmic means
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 itExpand
A note on the strong convergence of partial sums with respect to Vilenkin system
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system. 2010 Mathematics Subject Classification. 42C10.
On the Nörlund logarithmic means with respect to Vilenkin system in the martingale Hardy space H1
We prove and discuss a new divergence result of Nörlund logarithmic means with respect to Vilenkin system in Hardy space H1.
...
1
2
3
4
5
...