On boundedness and compactness of Riemann-Liouville fractional operators

Let α ∈ (0, 1). Consider the Riemann-Liouville fractional operator of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f \to T_\alpha f(x): = v(x)\int\limits_0^x {\frac{{f(y)u(y)dy}} {{(x - y)^{1 - \alpha } }}} ,x > 0, $\end{document} with locally integrable weight functions u and v. We find criteria for the Lp → Lq-boundedness and compactness of Tα when 0 < p,q < ∞, p > 1/α under the condition that u monotonely decreases on ℝ+:= [0,∞). The dual versions of this result are given.