scholarly journals Two-Weight Norm Inequality for the One-Sided Hardy-Littlewood Maximal Operators in Variable Lebesgue Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Caiyin Niu ◽  
Zongguang Liu ◽  
Panwang Wang
Keyword(s):  
Liouville Operator ◽  
Norm Inequality ◽  
Maximal Operators ◽  
Weight Norm Inequality ◽  
Weyl Operator ◽  
Lebesgue Spaces ◽  
Norm Inequalities ◽  
Variable Lebesgue Spaces ◽  
The One

The authors establish the two-weight norm inequalities for the one-sided Hardy-Littlewood maximal operators in variable Lebesgue spaces. As application, they obtain the two-weight norm inequalities of variable Riemann-Liouville operator and variable Weyl operator in variable Lebesgue spaces on bounded intervals.

Off-diagonal extrapolation on mixed variable Lebesgue spaces and its applications to strong fractional maximal operators

2020 ◽  
Vol 27 (4) ◽  
pp. 637-647
Author(s):  
Jian Tan
Keyword(s):  
Maximal Operators ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Lebesgue Spaces ◽  
Norm Inequalities ◽  
Variable Lebesgue Spaces ◽  
Vector Valued ◽  
Mixed Variable

AbstractWe establish off-diagonal extrapolation on mixed variable Lebesgue spaces. As its applications, we obtain the boundedness for strong fractional maximal operators. The vector-valued analogies are also considered. Additionally, the Littlewood–Paley characterization for mixed variable Lebesgue spaces is also established with the help of weighted norm inequalities and extrapolation.

Weighted Lorentz norm inequalities for general maximal operators associated with certain families of Borel measures

1998 ◽  
Vol 128 (2) ◽  
pp. 403-424 ◽  
Author(s):  
María Dolores Sarrión Gavilán
Keyword(s):  
Maximal Operator ◽  
Maximal Operators ◽  
Weighted Inequalities ◽  
General Measure ◽  
Norm Inequalities ◽  
Fractional Maximal Operator ◽  
Borel Measures ◽  
The One ◽  
Littlewood Maximal Operator ◽  
Lorentz Norm

Given a certain family ℱ of positive Borel measures and γ ∈ [0, 1), we define a general onesided maximal operatorand we study weighted inequalities inLp,qspaces for these operators. Our results contain, as particular cases, the characterisation of weighted Lorentz norm inequalities for some well-known one-sided maximal operators such as the one-sided Hardy–Littlewood maximal operator associated with a general measure, the one-sided fractional maximal operatorand the maximal operatorassociated with the Cesèro-α averages.

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