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.