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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 621857, 5 pages
http://dx.doi.org/10.1155/2014/621857
Research Article

Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Spaces

1Department of Mathematics, University of Malakand, Chakdara, Lower Dir 18800, Pakistan
2Department of Mathematics, GC University, Faisalabad, Faisalabad 38000, Pakistan

Received 23 May 2014; Accepted 6 August 2014; Published 26 August 2014

Academic Editor: Norio Yoshida

Copyright © 2014 Muhammad Sarwar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

One-weight inequalities with general weights for Riemann-Liouville transform and -dimensional fractional integral operator in variable exponent Lebesgue spaces defined on are investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of nonnegative decreasing functions in spaces.