One and two weight norm inequalities for Riesz potentials

By D. Cruz-Uribe, Kabe Moen. 2012

56 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a2de97b71cac8058410d9e6bc4893f7b8df4e619

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In Applied Mathematics

1. D. Cruz-Uribe
2. Kabe Moen
3. Sfo
4. Andrei K. Lerner
5. Dachun Yang
6. Tuomas Hytönen
7. C. P'erez
8. Ciqiang Zhuo

In Numerical Analysis

1. D. Cruz-Uribe
2. Sfo
3. Kabe Moen

Citations in the corpus

• A Fractional Muckenhoupt–Wheeden Theorem and its Consequences (2013, methodology): “2 made by us in an earlier paper [5].”
• Sharp weighted bounds without testing or extrapolation (2012, background): “ng sparse families of cubes. We begin with the simpler operator Iα. Given a dyadic grid D and 0 &lt; α &lt; n, define the dyadic fractional integral operator as ID α f := X Q∈D |Q|αn − Z Q f dx·χQ. In [3] it is proven that there exists a finite collection of dyadic grids D1,...,DN such that (3) Iαf ≃ ”
• Two weight norm inequalities for fractional integral operators and commutators (2014, methodology): “[24] D. Cruz-Uribe and K. Moen.”