相关论文: On The maximal operators of Vilenkin-Fej\'er means
The main aim of this paper is to prove that when $0<p<1/2$ the maximal operator $\overset{\sim }{\sigma }_{p}^{\ast }f:=\underset{n\in \mathbb{N}}{% \sup }\frac{\left\vert \sigma_{n}f\right\vert }{\left( n+1\right) ^{1/p-2}}$ is bounded…
The main aim of this paper is to prove that the maximal operator $\sigma_{p}^{\kappa ,\ast }f:=\sup_{n\in \mathbf{P}}\left\vert \sigma_{n}^{\kappa }f\right\vert /\left( n+1\right) ^{1/p-2}$ is bounded from the Hardy space $% H_{p}$ to the…
In this paper we derive the maximal subspace of positive numbers, for which the restricted maximal operator of Fej\'er means in this subspace is bounded from the Hardy space $H_{p}$ to the space $L_{p}$ for all $0<p\leq 1/2.$ Moreover, we…
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…
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…
The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space $%H_{p}$ to the Lebesgue…
The main aim of this paper is to investigate (H_{p},L_{p})-type inequalities for maximal operators of logarithmic means of one-dimensional Vilenkin-Fourier series.
The properties of the maximal operator of the $(C,\alpha)$-means ($\alpha=(\alpha_1,\ldots,\alpha_d)$) of the multi-dimensional Walsh-Kaczmarz-Fourier series are discussed, where the set of indices is inside a cone-like set. We prove that…
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 main aim of this paper is to investigate $\left( H_{p},L_{p}\right) $ and $\left( H_{p},L_{p,\infty }\right) $ type inequalities for maximal operators of Riesz logarithmic means of one-dimensional Vilenkin-Fourier series.
The main aim of this paper is to investigate $\left(H_{p},L_{p}\right)$- type inequalities for the the maximal operators of N\"orlund logaritmic means, for $0<p<1.$
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…
It is proved that the operators $\sigma_{n}^{\bigtriangleup}$ of the triangular-Fej{\'e}r-means of a two-dimensional Walsh--Fourier series are uniformly bounded from the dyadic Hardy space $H_{p}$ to $L_{p}$ for all $% 4/5<p\leq \infty $.
In this paper, we introduce a criterion for maximal operators associated with Fourier multipliers to be bounded on $L^p(\mathbb{R}^d)$. Noteworthy examples satisfying the criterion are multipliers of the Mikhlin type or limited decay which…
TThe main aim of this paper is to prove that there exist a martingale $f\in H_{1/2}$ such that Fej\'er means of Vilenkin-Fourier series of the martingale $f$ is not uniformly bounded in the space $L_{1/2}.$
In this paper we characterize subsequences of Fej\'er 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 result is in a sense sharp.
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…
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Fej\'er means in terms of the modulus of continuity on the Hardy spaces $H_{p},$ when $0<p\leq 1/2.$
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<p\leq 1/2.$
Let $1<p\leq \infty$ and let $n\geq 2.$ It was proved independently by C. Calder\'on, R. Coifman and G. Weiss that the dyadic maximal function \begin{equation*}…