SHARP WEIGHTED BOUNDS FOR FRACTIONAL INTEGRAL OPERATORS

By Michael T. Lacey, Kabe Moen, C. P'erez, Rodolfo H. Torres. 2009

141 citations recorded by the source corpus.

Abstract The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c1dd3c0b4da6490abcc6a9b2dd948f11c3e55277

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Kabe Moen
2. D. Cruz-Uribe
3. Andrei K. Lerner
4. Tuomas Hytönen
5. C. P'erez
6. P. Hasto
7. Kangwei Li
8. Michael T. Lacey

In Numerical Analysis

1. D. Cruz-Uribe
2. Kabe Moen

Citations in the corpus

• A Fractional Muckenhoupt–Wheeden Theorem and its Consequences (2013, unknown): “This case was studied in [14].”
• Sharp weighted bounds without testing or extrapolation (2012, background): “2 KABE MOEN new proof of the bound from [12], (2) ‖Iα‖B(Lp(wp),Lq(wq)) ≤ cp,α[w] (1− n )max(1, p ′ q ) Ap,q , for a range of p and q that satisfy 1 q = 1 p − α n .”
• Two weight norm inequalities for fractional integral operators and commutators (2014, background): “[51], and first appeared explicitly in [25], where the following result was proved.”
• One and two weight norm inequalities for Riesz potentials (2012, background): “More recently, the second author with Lacey, Pérez and Torres [20] proved sharp bounds for these inequalities in terms of the [w]Ap,q constant.”