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A Weighted Variant of Riemann‐Liouville Fractional Integrals on ℝn

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  • Zun Wei Fu
  • Shan Zhen Lu
  • Wen Yuan

Abstract

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.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:780132
DOI: 10.1155/2012/780132
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