Almost everywhere convergence of sequences of two-dimensional Walsh–Fejér means of integrable functions

2011 ◽  
Vol 134 (4) ◽  
pp. 589-601
Author(s):  
György Gát
Keyword(s):  
Two Dimensional ◽  
Almost Everywhere Convergence ◽  
Fejér Means ◽  
Almost Everywhere ◽  
Integrable Functions ◽  
Convergence Of Sequences

Almost everywhere convergence of some subsequences of Fejér means for integrable functions on some unbounded Vilenkin groups

2017 ◽  
Vol 67 (1) ◽  
Author(s):  
Nacima Memić
Keyword(s):  
Almost Everywhere Convergence ◽  
Fejér Means ◽  
Vilenkin Groups ◽  
Almost Everywhere ◽  
Integrable Functions

AbstractFollowing the methods of G. Gát, in this work we prove the a.e convergence of the subsequence

APPLICATIONS OF MULTI-PARAMETER MARTINGALES IN FOURIER ANALYSIS

2011 ◽  
Vol 11 (02n03) ◽  
pp. 551-568
Author(s):  
FERENC WEISZ
Keyword(s):  
Fourier Series ◽  
Fourier Analysis ◽  
Two Dimensional ◽  
Almost Everywhere Convergence ◽  
Fejér Means ◽  
Almost Everywhere ◽  
L Log L

With the help of the theory of multi-parameter martingales we prove almost everywhere convergence of the Fejér means of two-dimensional Walsh–Fourier series of f ∈ L log L.

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.

Sign in / Sign up

Export Citation Format

Share Document