相关论文: Strong Summability of Two-Dimensional Vilenkin Fou…

In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh-Kaczmarz-Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh-Kaczmarz-Fourier…

In this paper we investigate convergence and strong summability of the two-dimensional Vilenkin-Fourier series in the martingale Hardy spaces.

In this paper we study the a.e. exponential strong summability problem for the rectangular partial sums of double trigonometric Fourier series of the functions from $L\log L$ .

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.

We prove that certain means of the quadratical partial sums of the two-dimensional Vilenkin-Fourier series are uniformly bounded operators from the Hardy space $H_{p}$ to the space $L_{p}$ for $0<p\leq 1.$ We also prove that the sequence in…

It is proved a BMO-estimation for quadratic partial sums of two-dimensional Walsh-Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Walsh-Fourier series.

In this paper we study the a. e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. Namely, we prove the a.e. relation $(\frac{1}{n}\sum\limits_{m=0}^{n-1}\left\vert S_{mm}f - f…

It is proved a BMO-estimation for rectangular partial sums of two-dimensional Walsh-Fourier series from which it is derived an almost everywhere exponential summability of rectangular partial sums of double Walsh-Fourier series.

Let $S_{n}f$ denote the $n$th partial sum of the Vilenkin-Fourier series of a function $f \in L^{1}(G)$. For $1 < p_{-} \leq p_{+} < \infty$, we characterize all exponents $p(\cdot)$ for which the convergence of $S_{n}f$ to $f$ in…

We prove a Korovkin type approximation theorem via power series methods of summability for continuous $2\pi$-periodic functions of two variables and verify the convergence of approximating double sequences of positive linear operators by…

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

A trigonometric series strongly bounded at two points and with coefficients forming a log-quasidecreasing sequence is necessarily the Fourier series of a function belonging to all $L^{p}$ spaces, $1\leq p < \infty$. We obtain new results on…

The Fourier series of continuous functions of constant absolute value have interesting properties : according to the main theorems of the article, if the coefficients with positive indexes are square-summable with respect to a certain…

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

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…

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.

The main aim of this paper is to investigate the quadratical partial sums of the two-dimensional Walsh-Fourier series.

We prove that if a multiple trigonometric series is spherically Abel summable everywhere to an everywhere finite function $f(x)$ which is bounded below by an integrable function, then the series is the Fourier series of $f(x)$ if the…

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…

As main result we prove strong convergence theorems of Vilenkin-Fej\'er means when $0<p\leq 1/2.$