One and two weight norm inequalities for Riesz potentials

@article{CruzUribe2012OneAT,
  title={One and two weight norm inequalities for Riesz potentials},
  author={David Cruz-Uribe and Kabe Moen},
  journal={arXiv: Classical Analysis and ODEs},
  year={2012}
}
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… 
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