A Weighted Variant of Riemann-Liouville Fractional Integrals on R^n

We introduce certain type of weighted variant of Riemann‐Liouville fractional integral on ℝ n 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 operato...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2012-01, Vol.2012 (1), p.215-232-615
Main Authors: Fu, Zun Wei, Lu, Shan Zhen, Yuan, Wen
Format: Article
Language:English
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Summary:We introduce certain type of weighted variant of Riemann‐Liouville fractional integral on ℝ n 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