Riemann-Liouville and higher dimensional Harday operators for non-negative decreasing function in $L^{p(\cdot)}$ spaces

Abstract

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 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.