On the almost everywhere convergence of double Fourier series of integrable functions

1985 ◽  
Vol 11 (3) ◽  
pp. 201-216 ◽  
Author(s):  
М. Г. Григорян
Keyword(s):  
Fourier Series ◽  
Double Fourier Series ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere ◽  
Integrable Functions

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.

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 .

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