arXiv subjects

Davit Baramidze

Publications and source records attributed to Davit Baramidze.

6 recordsLinked to original sources

arXiv2023

On some weighted maximal operators of partial sums of Walsh-Fourier series in the space $H_1$

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 Walsh-Fourier series. We prove that for some "optimal" weights these new operators indeed are bounded from the martingale Hardy space $H_{1}(G)$ to the space $\text{weak}-L_{1}(G),$ but is not bounded from $H_{1}(G)$ to the space $L_{1}(G).$

math.FA↗

arXiv2023

Weighted maximal operators of Fejér means of Walsh-Fourier series in the martingale Hardy space $H_{1/2}$

In this paper we derive the restricted weighted maximal operator, defined by ${\sup }_{k\in \mathbb{N}}\left(\left\vert σ_{k}F\right\vert/A^2_k\right)$ of Fejér means of Walsh-Fourier series and prove that the it is bounded from the martingale Hardy space $H_{1/2}(G)$ to the Lebesgue space $L_{1/2}(G).$ The sharpness of this result is also proved. As a consequence we obtain some new and and well-know results.

math.CA↗

arXiv2023

Some new restricted maximal operators of Fejér means of Walsh-Fourier series in the space $H_{1/2}$

In this paper we derive the maximal subspace of natural numbers $\left\{n_{k}:k\geq 0\right\}$, such that the restricted maximal operator, defined by $\sup_{k\in \mathbb{N}}\left\vert σ_{n_{k}}F \right\vert$ on this subspace of Fejér means of Walsh-Fourier series is bounded from the martingale Hardy space $H_{1/2}$ to the Lebesgue space $L_{1/2}$. The sharpness of this result is also proved.

math.CA↗

arXiv2022

Sharp $(H_p,L_p)$ and $(H_p,\text{weak}-L_p)$ type inequalities of weighted maximal operators of $T$ means with respect to Vilenkin systems

We discuss $(H_p,L_p)$ and $(H_p,\text{weak}-L_p)$ type inequalities of weighted maximal operators of $T$ means with respect to the Vilenkin systems with monotone coefficients, considered in \cite{tut4} and prove that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out.

math.CA↗

arXiv2022

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

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 $T$ means.

math.CA↗

arXiv2022

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

In this paper we derive converge of Nörlund 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 Nörlund means.

math.CA↗