arXiv subjects

György Gát

Publications and source records attributed to György Gát.

4 recordsLinked to original sources

arXiv2018

Cesàro means of subsequences of partial sums of trigonometric Fourier series

In 1936 Zygmunt Zalcwasser asked with respect to the trigonometric system that how "rare" can a sequence of strictly monotone increasing integers $(n_j)$ be such that the almost everywhere relation $\frac{1}{N}\sum_{j=1}^N S_{n_j}f \to f$ is fulfilled for each integrable function $f$. In this paper, we give an answer to this question. It follows from the main result that this a.e. relation holds for every integrable function $f$ and lacunary sequence $(n_j)$ of natural numbers.

math.CA↗

arXiv2017

Almost everywhere convergence of Fejér means of two-dimensional triangular Walsh-Fourier series

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 investigate the Fejér (or $(C,1)$) means of the triangle two variable Walsh-Fourier series of $L^1$ functions. Namely, we prove the a.e. convergence $σ_n^{\bigtriangleup}f = \frac{1}{n}\sum_{k=0}^{n-1}S_{k, n-k}f\to f$ ($n\to\infty$) for each integrable two-variable function $f$.

math.CA↗

arXiv2014

Convergence of logarithmic means of Multiple Walsh-Fourier series

The maximal Orlicz spaces such that the mixed logarithmic means of multiple Walsh-Fourier series for the functions from these spaces converge in measure and in norm are found.

math.AP↗

arXiv2013

Triangular Fejér Summability of Two-Dimensional Walsh-Fourier series

It is proved that the operators $σ_{n}^{\bigtriangleup}$ of the triangular-Fej{é}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 $.

math.AP↗