Abstract:In this paper we give a sufficient condition on the pair of weights $(w,v)$ for the boundedness of the Weyl fractional integral $I_{\alpha }^+$ from $L^p(v)$ into $L^p(w)$. Under some restrictions on $w$ and $v$, this condition is also necessary. Besides, it allows us to show that for any $p: 1 \leq p < \infty $ there exist non-trivial weights $w$ such that $I_{\alpha }^+$ is bounded from $L^p(w)$ into itself, even in the case $\alpha > 1$.
Keywords: Weyl fractional integrals, weights
AMS Subject Classification: Primary 26A33; Secondary 42B25