Zobrazeno 1 - 10
of 179
pro vyhledávání: '"TEPHNADZE, GEORGE"'
In this paper 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 $H_{p}$ to the Lebesgue sp
Externí odkaz:
http://arxiv.org/abs/2308.00794
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 the marti
Externí odkaz:
http://arxiv.org/abs/2303.01846
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 $\sup_{k\in \mathbb{N}}\left\vert \sigma_{n_{k}}F \right\vert$ on this subspace of Fej\'er means of
Externí odkaz:
http://arxiv.org/abs/2302.12997
In this paper we derive the restricted weighted maximal operator, defined by ${\sup }_{k\in \mathbb{N}}\left(\left\vert \sigma _{k}F\right\vert/A^2_k\right)$ of Fej\'er means of Walsh-Fourier series and prove that the it is bounded from the martingal
Externí odkaz:
http://arxiv.org/abs/2302.12302
The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are also deri
Externí odkaz:
http://arxiv.org/abs/2302.12298
As main result we prove that Fej\'er means of Walsh-Kaczmarz-Fourier series are uniformly bounded operators from the Hardy martingale space $\ H_{p}$ to the Hardy martingale space $H_{p}$ for $ 0
Externí odkaz:
http://arxiv.org/abs/2008.07526
Autor:
Tephnadze, George
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 applications, b
Externí odkaz:
http://arxiv.org/abs/2008.00941
Autor:
Gogolashvili, Nata, Tephnadze, George
In this paper we prove and discuss some new $\left( H_p,L_{p,\infty}\right)$ type inequalities of the maximal operators of $T$ means with monotone coefficients with respect to Walsh-Kaczmarz system. It is also proved that these results are the best p
Externí odkaz:
http://arxiv.org/abs/2007.14455
Autor:
Tephnadze, George
In this paper we investigate strong summability of the two-dimensional Walsh-Fourier series obtained in Weisz \cite{We} (see Theorem W) and prove sharpness of this result.
Externí odkaz:
http://arxiv.org/abs/2002.03768
Autor:
Tephnadze, George
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 achieve the foll
Externí odkaz:
http://arxiv.org/abs/1902.06696