%0 Journal Article
%T One and two weight norm inequalities for Riesz potentials
%A David Cruz-Uribe
%A Kabe Moen
%J Mathematics
%D 2012
%I arXiv
%X We consider weighted norm inequalities for the Riesz potentials $I_\alpha$, also referred to as fractional integral operators. First we prove mixed $A_p$-$A_\infty$ type estimates in the spirit of [13, 15, 17]. Then we prove strong and weak type inequalities in the case $p<q$ using the so-called log bump conditions. These results complement the strong type inequalities of P\'erez [30] and answer a conjecture from [3]. For both sets of results our main tool is a corona decomposition adapted to fractional averages.
%U http://arxiv.org/abs/1207.5551v2