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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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.

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

First available in Project Euclid: 5 April 2013

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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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