scholarly journals Fractional maximal operator in Orlicz spaces

2019 ◽  
Vol 474 (1) ◽  
pp. 94-115 ◽  
Author(s):  
Vít Musil
Keyword(s):  
Maximal Operator ◽  
Orlicz Spaces ◽  
Fractional Maximal Operator

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

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

New Proofs of Two-Weight Norm Inequalities for the Maximal Operator

2000 ◽  
Vol 7 (1) ◽  
pp. 33-42 ◽  
Author(s):  
D. Cruz-Uribe
Keyword(s):  
Maximal Operator ◽  
Sufficient Conditions ◽  
Norm Inequality ◽  
Strong Type ◽  
Norm Inequalities ◽  
Fractional Maximal Operator ◽  
Littlewood Maximal Operator

Abstract We give a new and simpler proof of Sawyer's theorem characterizing the weights governing the two-weight, strong-type norm inequality for the Hardy-Littlewood maximal operator and the fractional maximal operator. As a further application of our techniques, we give new proofs of two sufficient conditions for such weights due to Wheeden and Sawyer.

scholarly journals Mapping properties of the discrete fractional maximal operator in metric measure spaces

2013 ◽  
Vol 53 (3) ◽  
pp. 693-712 ◽  
Author(s):  
Toni Heikkinen ◽  
Juha Kinnunen ◽  
Juho Nuutinen ◽  
Heli Tuominen
Keyword(s):  
Maximal Operator ◽  
Metric Measure Spaces ◽  
Fractional Maximal Operator ◽  
Measure Spaces

scholarly journals Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Emin V. Guliyev ◽  
Yagub Y. Mammadov
Keyword(s):  
Maximal Operator ◽  
Morrey Space ◽  
Shift Operator ◽  
Morrey Spaces ◽  
Dunkl Operator ◽  
Generalized Shift Operator ◽  
Fractional Maximal Operator ◽  
Generalized Shift

We consider the generalized shift operator, associated with the Dunkl operatorΛα(f)(x)=(d/dx)f(x)+((2α+1)/x)((f(x)-f(-x))/2),α>-1/2. We study some embeddings into the Morrey space (D-Morrey space)Lp,λ,α,0≤λ<2α+2and modified Morrey space (modifiedD-Morrey space)L̃p,λ,αassociated with the Dunkl operator onℝ. As applications we get boundedness of the fractional maximal operatorMβ,0≤β<2α+2, associated with the Dunkl operator (fractionalD-maximal operator) from the spacesLp,λ,αtoL∞(ℝ)forp=(2α+2-λ)/βand from the spacesL̃p,λ,α(ℝ)toL∞(ℝ)for(2α+2-λ)/β≤p≤(2α+2)/β.

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