A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn

We introduce certain type of weighted variant of Riemann-Liouville fractional integral on ℝn and obtain its sharp bounds on the central Morrey and λ-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators...

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Bibliographic Details
Published in:Abstract and applied analysis 2012-01, Vol.2012 (2012), p.1-18
Main Authors: Fu, Zun Wei, Lu, Shan Zhen, Yuan, Wen
Format: Article
Language:English
Subjects:
Commutators
Estimates
Inequalities
Integrals
Operators
Symbols
Weight function
Online Access:Get full text
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Summary:We introduce certain type of weighted variant of Riemann-Liouville fractional integral on ℝn and obtain its sharp bounds on the central Morrey and λ-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators (with symbols in λ-central BMO space) are bounded on the central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Weyl and Cesàro.
ISSN:1085-3375
1687-0409
DOI:10.1155/2012/780132