相关论文: Almost Everywhere Strong Summability of two-dimens…
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.
It is proved a $BMO$-estimation for quadratic partial sums of two-dimensional Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double 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…
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.
The main aim of this paper is to investigate the quadratical partial sums of the two-dimensional Walsh-Fourier series.
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 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 study the exponential uniform strong summability of two-dimensional Vilenkin-Fourier series. In particular, it is proved that the two-dimensional Vilenkin-Fourier series of the continuous function $f$ is uniformly strong…
We prove that certain mean of the quadratical partial sums of the two-dimensional Walsh-Fourier series are uniformly bounded operators from the Hardy space $H_{p}$ to the space $L_{p}$ for $0<p<1.$
The convergence of partial sums and Ces\'aro means of negative order of double Walsh-Fourier series of functions of bounded \ generalized variation is investigated.
We prove an exponential integral estimate for the quadratic partial sums of multiple Fourier series on large sets that implies some new properties of Fourier series.
Almost everywhere strong exponential summability of Fourier series in Walsh and trigonometric systems established by Rodin in 1990. We prove, that if the growth of a function $\Phi(t):[0,\infty)\to[0,\infty)$ is bigger than the exponent,…
In this paper we investigate convergence and strong summability of the two-dimensional Vilenkin-Fourier series in the martingale Hardy spaces.
This article establishes a real-variable argument for Zygmund's theorem on almost everywhere convergence of strong arithmetic means of partial sums of Fourier series on $\mathbb{T}$, up to passing to a subsequence. Our approach extends to,…
In 1987 Harris proved (Proc. Amer. Math. Soc., 101) - among others- that for each $1\le p<2$ there exists a two-dimensional function $f\in L^p$ such that its triangular Walsh-Fourier series diverges almost everywhere. In this paper we…
Let $S_m f$ denote the $m$-th partial sum of the Walsh-Fourier series of $f \in L^1$. For an increasing sequence $a=(a(n))_{n \geq 1}$ of positive integers, consider the arithmetic means $$ \sigma_N f:=\frac{1}{N} \sum_{n=1}^N S_{a(n)} f .…
We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of almost periodic functions from matrix means of partial sums of their Fourier series.
In this paper we investigate some convergence and divergence of some specific subsequences of partial sums with respect to Walsh system on the martingale Hardy spaces. By using these results we obtain relationship of the ratio of…
In this paper we present results on convergence and Ces\`{a}ro summability of Multiple Fourier series of functions of bounded generalized variation.
We establish two general theorems on the local properties of the absolute summability of factored Fourier series by applying a recently defined absolute summability, $\left\vert A,\alpha_{n}\right\vert _{k}$ summability, and the class…