Maximal operator of the Fejér means of triangular partial sums of two-dimensional Walsh–Fourier series

2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Ushangi Goginava ◽  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Maximal Operator ◽  
Partial Sums ◽  
Two Dimensional ◽  
Fejér Means

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.

scholarly journals Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series

2010 ◽  
Vol 8 (2) ◽  
pp. 181-200
Author(s):  
Ushangi Goginava ◽  
Károly Nagy
Keyword(s):  
Fourier Series ◽  
Maximal Operator ◽  
Maximal Operators ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Fejér Means

The main aim of this paper is to prove that there exists a martingalef∈H1/2such that the maximal Fejér operator with respect to Walsh-Kaczmarz system does not belong to the spaceL1/2. For the two-dimensional case, we prove that there exists a martingalef∈H1/2□(f∈H1/2)such that the restricted (unrestricted) maximal operator of Fejér means of two-dimensional Walsh-Kaczmarz-Fourier series does not belong to the space weak-L1/2.

The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

2008 ◽  
Vol 45 (3) ◽  
pp. 321-331
Author(s):  
István Blahota ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Maximal Operator ◽  
Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

Sign in / Sign up

Export Citation Format

Share Document