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arXiv · 1207.5551

One and two weight norm inequalities for Riesz potentials

David Cruz-Uribe·Kabe Moen
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Abstract

We consider weighted norm inequalities for the Riesz potentials $I_α$, 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 Pérez [30] and answer a conjecture from [3]. For both sets of results our main tool is a corona decomposition adapted to fractional averages.

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David Cruz-Uribe, Kabe Moen. 2012-11-15. One and two weight norm inequalities for Riesz potentials. https://arxiv.org/abs/1207.5551

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