Riemann-Liouville and higher dimensional Harday operators for   non-negative decreasing function in $L^{p(\cdot)}$ spaces
  In this paper one-weight inequalities with general weights for Riemann-Liouville transform and $ n-$ dimensional fractional integral operator in variable exponent Lebesgue spaces defined on $\mathbb{R}^{n}$ are investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of non-negative decreasing functions in $L^{p(x)}$ spaces. 
Ghulam Murtaza and Muhammad Sarwar
math.FA