Hardy-Type Operators in Lorentz-Type Spaces Defined on Measure Spaces

2020 ◽  
Vol 51 (3) ◽  
pp. 1105-1132
Author(s):  
Qinxiu Sun ◽  
Xiao Yu ◽  
Hongliang Li
Keyword(s):  
Hardy Type ◽  
Measure Spaces ◽  
Type Spaces ◽  
Hardy Type Operators

Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces

2021 ◽  
Vol 24 (6) ◽  
pp. 1643-1669
Author(s):  
Natasha Samko
Keyword(s):  
Upper Bound ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Target Space ◽  
Metric Measure Spaces ◽  
Generalized Morrey Spaces ◽  
Hardy Type ◽  
Measure Spaces ◽  
Hardy Operators ◽  
Hardy Type Operators

Abstract We study commutators of weighted fractional Hardy-type operators within the frameworks of local generalized Morrey spaces over quasi-metric measure spaces for a certain class of “radial” weights. Quasi-metric measure spaces may include, in particular, sets of fractional dimentsions. We prove theorems on the boundedness of commutators with CMO coefficients of these operators. Given a domain Morrey space 𝓛 p,φ (X) for the fractional Hardy operators or their commutators, we pay a special attention to the study of the range of the exponent q of the target space 𝓛 q,ψ (X). In particular, in the case of classical Morrey spaces, we provide the upper bound of this range which is greater than the known Adams exponent.

The supremum-involving Hardy-type operators on Lorentz-type spaces

2020 ◽  
Vol 77 (1) ◽  
pp. 1-29
Author(s):  
Qinxiu Sun ◽  
Xiao Yu ◽  
Hongliang Li
Keyword(s):  
Hardy Type ◽  
Type Spaces ◽  
Hardy Type Operators

scholarly journals The boundedness of commutators of rough p-adic fractional Hardy type operators on Herz-type spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amjad Hussain ◽  
Naqash Sarfraz ◽  
Ilyas Khan ◽  
Abdelaziz Alsubie ◽  
Nawaf N. Hamadneh
Keyword(s):  
Function Spaces ◽  
Type Operator ◽  
Hardy Type ◽  
Type Spaces ◽  
Hardy Type Operator ◽  
Hardy Type Operators

AbstractIn this paper, we obtain some inequalities about commutators of a rough p-adic fractional Hardy-type operator on Herz-type spaces when the symbol functions belong to two different function spaces.

On weighted generalized fractional and Hardy-type operators acting between Morrey-type spaces

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Evgeniya Burtseva ◽  
Natasha Samko
Keyword(s):  
Morrey Spaces ◽  
Fractional Operators ◽  
Generalized Morrey Spaces ◽  
Hardy Type ◽  
Type Spaces ◽  
Hardy Type Operators

AbstractWe study weighted generalized Hardy and fractional operators acting from generalized Morrey spaces

scholarly journals Weighted Hardy-Type Inequalities in Variable Exponent Morrey-Type Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Dag Lukkassen ◽  
Lars-Erik Persson ◽  
Stefan Samko ◽  
Peter Wall
Keyword(s):  
Variable Exponent ◽  
Morrey Space ◽  
Variable Order ◽  
Generalized Morrey Space ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Radial Weight ◽  
Type Integral ◽  
Type Spaces ◽  
Hardy Type Operators

We study thep·→q·boundedness of weighted multidimensional Hardy-type operatorsHwα·andℋwα·of variable orderαx, with radial weightwx, from a variable exponent locally generalized Morrey spaceℒp·,φ·ℝn,wto anotherℒq·,ψ·ℝn,w. The exponents are assumed to satisfy the decay condition at the origin and infinity. We construct certain functions, defined byp,α, andφ, the belongness of which to the resulting spaceℒq·,ψ·ℝn,wis sufficient for such a boundedness. Under additional assumptions onφ/w, this condition is also necessary. We also give the boundedness conditions in terms of Zygmund-type integral inequalities for the functionsφandφ/w.

scholarly journals The Approximation Numbers of Hardy-Type Operators on Trees

2001 ◽  
Vol 83 (2) ◽  
pp. 390-418 ◽  
Author(s):  
W. D. Evans ◽  
D. J. Harris ◽  
J. Lang
Keyword(s):  
Approximation Numbers ◽  
Hardy Type ◽  
Hardy Type Operators

Atomic hardy-type spaces between H 1 and L 1 on metric spaces with non-doubling measures

2011 ◽  
Vol 27 (12) ◽  
pp. 2445-2468 ◽  
Author(s):  
Li Guang Liu ◽  
Da Chun Yang ◽  
Dong Yong Yang
Keyword(s):  
Metric Spaces ◽  
Hardy Type ◽  
Type Spaces ◽  
Doubling Measures
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