One and two weight norm inequalities for Riesz potentials

2013/01/01 by David Cruz-Uribe, SFO, SFO David Cruz-Uribe, Kabe Moen · 4 citations
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations

paper · pdf · doi:10.1215/ijm/1403534497

crossref issued 2013/01/01 · crossref published 2013/01/01 · crossref published-print 2013/01/01 · openalex publication_date 2013/01/01 · crossref created 2019/02/26 · crossref deposited 2024/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28 · crossref indexed 2026/07/29

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_∞ type estimates in the spirit of (Indiana Univ. Math. J. 61 (2012) 2041–2052, Anal. PDE 6 (2013) 777–818, Houston J. Math. 38 (2012) 799–814). 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 (Indiana Univ. Math. J. 43 (1994) 663–683) and answer a conjecture from (Weights, extrapolation and the theory of Rubio de Francia (2011) Birkhäuser). For both sets of results, our main tool is a corona decomposition adapted to fractional averages.

Citations

• Two Weight Inequalities for Discrete Positive Operators
• Weighted inequalities for the dyadic square function without dyadic A∞

Cited by

• Recent results on matrix weighted norm inequalities
• Extension of Multilinear Fractional Integral Operators to Linear\n Operators on Lebesgue Spaces with Mixed Norms
• Two weight norm inequalities for fractional integral operators and\n commutators
• A fractional Muckenhoupt-Wheeden theorem and its consequences

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