On Some (H p,q , L p,q )-Type Maximal Inequalities with Respect to the Walsh–Paley System

2000 ◽  
Vol 7 (3) ◽  
pp. 475-488 ◽  
Author(s):  
U. Goginava
Keyword(s):  
Fourier Series ◽  
Lorentz Space ◽  
Positive Cone ◽  
Maximal Operators ◽  
Maximal Inequalities ◽  
Paley System

Abstract The boundedness of Cesáro maximal operators for multiple Walsh–Fourier series is studied from the martingale Hardy–Lorentz space Hpq into the Lorentz space Lpq . Supremum in the maximal operators is taken over a positive cone.

On multipliers of Fourier series in the Lorentz space

2016 ◽  
Author(s):  
Aizhan Zh. Ydyrys ◽  
Nazerke T. Tleukhanova
Keyword(s):  
Fourier Series ◽  
Lorentz Space

On the boundedness of the maximal operators of double Walsh-logarithmic means of Marcinkiewicz type

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Ushangi Goginava ◽  
Károly Nagy
Keyword(s):  
Fourier Series ◽  
Type Inequality ◽  
Maximal Operators ◽  
Partial Sums ◽  
Logarithmic Means ◽  
P Type

AbstractThe main aim of this paper is to investigate the (H p, L p)-type inequality for the maximal operators of Riesz and Nörlund logarithmic means of the quadratical partial sums of Walsh-Fourier series. Moreover, we show that the behavior of Nörlund logarithmic means is worse than the behavior of Riesz logarithmic means in our special sense.

scholarly journals Characterizations of variable martingale Hardy spaces via maximal functions

2021 ◽  
Vol 24 (2) ◽  
pp. 393-420
Author(s):  
Ferenc Weisz
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Lorentz Space ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Continuity Condition ◽  
Maximal Functions ◽  
Maximal Operators ◽  
Special Cases ◽  
New Type

Abstract We introduce a new type of dyadic maximal operators and prove that under the log-Hölder continuity condition of the variable exponent p(⋅), it is bounded on L p(⋅) if 1 < p − ≤ p + ≤ ∞. Moreover, the space generated by the L p(⋅)-norm (resp. the L p(⋅), q -norm) of the maximal operator is equivalent to the Hardy space H p(⋅) (resp. to the Hardy-Lorentz space H p(⋅), q ). As special cases, our maximal operator contains the usual dyadic maximal operator and four other maximal operators investigated in the literature.

scholarly journals On the maximal operators of Riesz logarithmic means of Vilenkin-Fourier series

2014 ◽  
Vol 51 (1) ◽  
pp. 105-120
Author(s):  
George Tephnadze
Keyword(s):  
Fourier Series ◽  
Maximal Operators ◽  
One Dimensional ◽  
Logarithmic Means

The main aim of this paper is to investigate (Hp, Lp) and (Hp, Lp,∞) type inequalities for maximal operators of Riesz logarithmic means of one-dimensional Vilenkin—Fourier series.

scholarly journals Maximal operators of Fejér means of double Vilenkin–Fourier series

2007 ◽  
Vol 107 (2) ◽  
pp. 287-296 ◽  
Author(s):  
István Blahota ◽  
György Gát ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Maximal Operators ◽  
Fejér Means

scholarly journals Maximal summability operators on the dyadic hardy spaces

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2189-2208
Author(s):  
Ushangi Goginava ◽  
Salem Said
Keyword(s):  
Fourier Series ◽  
Hardy Spaces ◽  
Maximal Operators ◽  
Almost Everywhere Convergence ◽  
Varying Parameters ◽  
Almost Everywhere ◽  
Logarithmic Means

It is proved that the maximal operators of subsequences of N?rlund logarithmic means and Ces?ro means with varying parameters of Walsh-Fourier series is bounded from the dyadic Hardy spaces Hp to Lp. This implies an almost everywhere convergence for the subsequences of the summability means.

Marcinkiewicz-Fejér Means of double VIlenkin-Fourier series

2007 ◽  
Vol 44 (1) ◽  
pp. 97-115
Author(s):  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Lorentz Space ◽  
Maximal Operator ◽  
Fejér Means

The boundedness of the Marcinkiewicz maximal operator for double Vilenkin-Fourier series from the martingale Hardy-Lorentz space Hp,q into the Lorentz space Lp,q is studied.

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