## Abstract and Applied Analysis

### A Weighted Variant of Riemann-Liouville Fractional Integrals on ${\Bbb R}^{n}$

#### Abstract

We introduce certain type of weighted variant of Riemann-Liouville fractional integral on ${\Bbb R}^{n}$ and obtain its sharp bounds on the central Morrey and $\lambda$-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 $\lambda$-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

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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