On boundedness and compactness of Riemann–Liouville fractional operators

Let $\alpha\in(0,1)$. Consider the Riemann–Liouville fractional operator of the form
$$ f\to T_\alpha f(x):=v(x)\int_0^x\frac{f(y)u(y)\,dy}{(x-y)^{1-\alpha}},\qquad x>0, $$
with locally integrable weight functions $u$ and $v$. We find criteria for the $L^p\to L^q$-boundedness and compactness of $T_\alpha$ when $0<p,q<\infty$, $p>1/\alpha$ under the condition that $u$ monotonely decreases on $\mathbb R^+:=[0,1)$. The dual versions of this result are given.