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

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.

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

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2017-0081 ◽

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

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

Journal of Function Spaces and Applications ◽

10.1155/2013/716029 ◽

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.

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The Approximation Numbers of Hardy-Type Operators on Trees

Proceedings of the London Mathematical Society ◽

10.1112/plms/83.2.390 ◽

2001 ◽

Vol 83 (2) ◽

pp. 390-418 ◽

Cited By ~ 21

Author(s):

W. D. Evans ◽

D. J. Harris ◽

J. Lang

Keyword(s):

Approximation Numbers ◽

Hardy Type ◽

Hardy Type Operators

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Bernstein widths of Hardy-type operators in a non-homogeneous case

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.02.025 ◽

2007 ◽

Vol 325 (2) ◽

pp. 1060-1076 ◽

Cited By ~ 5

Author(s):

D.E. Edmunds ◽

J. Lang

Keyword(s):

Homogeneous Case ◽

Hardy Type ◽

Hardy Type Operators

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

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2021-0071 ◽

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.

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