Abstract and Applied Analysis

A Weighted Variant of Riemann-Liouville Fractional Integrals on n

Zun Wei Fu, Shan Zhen Lu, and Wen Yuan

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Abstract

We introduce certain type of weighted variant of Riemann-Liouville fractional integral on 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.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 780132, 18 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168352

Digital Object Identifier
doi:10.1155/2012/780132

Mathematical Reviews number (MathSciNet)
MR2970005

Zentralblatt MATH identifier
1253.26009

Citation

Fu, Zun Wei; Lu, Shan Zhen; Yuan, Wen. A Weighted Variant of Riemann-Liouville Fractional Integrals on ${\Bbb R}^{n}$. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 780132, 18 pages. doi:10.1155/2012/780132. https://projecteuclid.org/euclid.aaa/1365168352


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