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

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
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