scholarly journals Almost everywhere convergence of Cesàro means of two variable Walsh – Fourier series with varying parameteres

2021 ◽  
Vol 73 (3) ◽  
pp. 291-307
Author(s):  
A. A. Abu Joudeh ◽  
G. G´at
Keyword(s):  
Fourier Series ◽  
Maximal Operator ◽  
Weak Type ◽  
Partial Sums ◽  
Cesàro Means ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere ◽  
Integrable Functions ◽  
Walsh Group ◽  
Cesáro Means

UDC 517.5 We prove that the maximal operator of some means of cubical partial sums of two variable Walsh – Fourier series of integrable functions is of weak type . Moreover, the -means of the function converge a.e. to for , where is the Walsh group for some sequences .

Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series

2006 ◽  
Vol 13 (3) ◽  
pp. 447-462
Author(s):  
György Gát ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Maximal Operator ◽  
Weak Type ◽  
Partial Sums ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere

Abstract We prove that the maximal operator of the (𝐶, α)-means of quadratical partial sums of double Vilenkin–Fourier series is of weak type (1,1). Moreover, the (𝐶, α)-means of a function 𝑓 ∈ 𝐿1 converge a.e. to 𝑓 as 𝑛 → ∞.

scholarly journals Almost everywhere convergence and divergence of Cesàro means with varying parameters of Walsh–Fourier series

2021 ◽  
Author(s):  
György Gát ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Cesàro Means ◽  
Almost Everywhere Convergence ◽  
Varying Parameters ◽  
Cesaro Means ◽  
Almost Everywhere ◽  
Cesáro Means ◽  
Convergence And Divergence

AbstractIn the present paper, we prove the almost everywhere convergence and divergence of subsequences of Cesàro means with zero tending parameters of Walsh–Fourier series.

scholarly journals Almost everywhere convergence of a subsequence of the logarithmic means of Vilenkin-Fourier series

2008 ◽  
Vol 21 (3) ◽  
pp. 275-289
Author(s):  
György Gát ◽  
Károly Nagy
Keyword(s):  
Fourier Series ◽  
Maximal Operator ◽  
Weak Type ◽  
Integrable Function ◽  
Partial Sums ◽  
One Dimensional ◽  
Almost Everywhere ◽  
Logarithmic Means ◽  
The One

The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Vilenkin-Fourier series is of weak type (1, 1). Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1, 1), provided that the supremum in the maximal operator is taken over special indices. The set of Vilenkin polynomials is dense in L1, so by the well-known density argument the logarithmic means t2n(f) converge a.e. to f for all integrable function f. .

Convergence of Marcinkiewicz Means of Integrable Functions with Respect to Two-Dimensional Vilenkin Systems

2004 ◽  
Vol 11 (3) ◽  
pp. 467-478
Author(s):  
György Gát
Keyword(s):  
Maximal Operator ◽  
Weak Type ◽  
Integrable Function ◽  
Two Dimensional ◽  
Vilenkin Groups ◽  
Almost Everywhere ◽  
Integrable Functions ◽  
Marcinkiewicz Means

Abstract We prove that the maximal operator of the Marcinkiewicz mean of integrable two-variable functions is of weak type (1, 1) on bounded two-dimensional Vilenkin groups. Moreover, for any integrable function 𝑓 the Marcinkiewicz mean σ 𝑛𝑓 converges to 𝑓 almost everywhere.

scholarly journals Walsh-Fourier series with coefficients of generalized bounded variation

1989 ◽  
Vol 47 (3) ◽  
pp. 458-465 ◽  
Author(s):  
F. Móricz
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Real Numbers ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere ◽  
Integrable Functions

AbstractWe extend in different ways the class of null sequences of real numbers that are of bounded variation and study the Walsh-Fourier series of integrable functions on the interval [(0, 1) with such coefficients. We prove almost everywhere convergence as well as convergence in the pseu dometric of Lr(0, 1) for 0 < r < 1.

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