Weighted Inequalities for the Fractional Maximal Operator in Lorentz Spaces via Atomic Decomposition of Tent Spaces

1997 ◽  
Vol 16 (2) ◽  
pp. 263-280
Author(s):  
Y. Rakotondratsimba
Keyword(s):  
Maximal Operator ◽  
Atomic Decomposition ◽  
Lorentz Spaces ◽  
Weighted Inequalities ◽  
Tent Spaces ◽  
Fractional Maximal Operator

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.

Riesz potential in the local Morrey–Lorentz spaces and some applications

2020 ◽  
Vol 27 (4) ◽  
pp. 557-567
Author(s):  
Vagif S. Guliyev ◽  
Abdulhamit Kucukaslan ◽  
Canay Aykol ◽  
Ayhan Serbetci
Keyword(s):  
Maximal Operator ◽  
Riesz Potential ◽  
Sufficient Conditions ◽  
Lorentz Spaces ◽  
Necessary And Sufficient Conditions ◽  
Analytic Semigroups ◽  
Fractional Powers ◽  
Marcinkiewicz Operator ◽  
Fractional Maximal Operator ◽  
Necessary And Sufficient

AbstractIn this paper, the necessary and sufficient conditions are found for the boundedness of the Riesz potential {I_{\alpha}} in the local Morrey–Lorentz spaces {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})}. This result is applied to the boundedness of particular operators such as the fractional maximal operator, fractional Marcinkiewicz operator and fractional powers of some analytic semigroups on the local Morrey–Lorentz spaces {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})}.

Boundedness of the fractional maximal operator in local Morrey-type spaces

2010 ◽  
Vol 55 (8-10) ◽  
pp. 739-758 ◽  
Author(s):  
V.I. Burenkov ◽  
A. Gogatishvili ◽  
V.S. Guliyev ◽  
R.Ch. Mustafayev
Keyword(s):  
Maximal Operator ◽  
Fractional Maximal Operator ◽  
Type Spaces

Commutators of Fractional Maximal Operator on Orlicz Spaces

2018 ◽  
Vol 104 (3-4) ◽  
pp. 498-507
Author(s):  
V. S. Guliyev ◽  
F. Deringoz ◽  
S. G. Hasanov
Keyword(s):  
Maximal Operator ◽  
Orlicz Spaces ◽  
Fractional Maximal Operator
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