Pointwise convergence of cone-like restricted two-dimensional Fejér means of Walsh-Fourier series

2010 ◽  
Vol 26 (12) ◽  
pp. 2295-2304 ◽  
Author(s):  
György Gát ◽  
Károly Nagy
Keyword(s):  
Fourier Series ◽  
Pointwise Convergence ◽  
Two Dimensional ◽  
Fejér Means

Pointwise convergence of Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series

2012 ◽  
Vol 49 (2) ◽  
pp. 236-253
Author(s):  
Ushangi Goginava ◽  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Pointwise Convergence ◽  
Two Dimensional ◽  
Fejér Means

In this paper we characterize the set of convergence of the Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series.

scholarly journals Convergence and divergence of Fejér means of Fourier series on one and two-dimensional Walsh and Vilenkin groups

2008 ◽  
Vol 21 (3) ◽  
pp. 291-307
Author(s):  
György Gát
Keyword(s):  
Fourier Series ◽  
Harmonic Analysis ◽  
Pointwise Convergence ◽  
Point Of View ◽  
Two Dimensional ◽  
Fejér Means ◽  
Vilenkin Groups ◽  
Recent Developments ◽  
Convergence And Divergence

It is a highly celebrated issue in dyadic harmonic analysis the pointwise convergence of the Fej?r (or (C, 1)) means of functions on the Walsh and Vilenkin groups both in the point of view of one and two dimensional cases. We give a resume of the very recent developments concerning this matter, propose unsolved problems and throw a glance at the investigation of Vilenkin-like systems too. .

A weak type inequality for the two-dimensional diagonal Sunouchi operator on the Hardy space

2011 ◽  
Vol 18 (1) ◽  
pp. 67-81
Author(s):  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Weak Type ◽  
Type Inequality ◽  
Partial Sums ◽  
Two Dimensional ◽  
Fejér Means ◽  
Weak Type Inequality

Abstract Define the two dimensional diagonal Sunouchi operator where S 2 n , 2 n ƒ and σ 2 n ƒ are the (2 n , 2 n )th cubic-partial sums and 2 n th Marcinkiewicz–Fejér means of a two-dimensional Walsh–Fourier series. The main aim of this paper is to prove that the operator is bounded from the Hardy space H 1/2 to the weak L 1/2 space and is not bounded from the Hardy space H 1/2 to the space L 1/2.

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