Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Lp(·) Spaces

Abstract

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 nonnegative decreasing functions in $L^{p(x)}$ spaces.