A Fractional Muckenhoupt–Wheeden Theorem and its Consequences

In the 1970s Muckenhoupt and Wheeden made several conjectures relating two weight norm inequalities for the Hardy-Littlewood maximal operator to such inequalities for singular integrals. Using techniques developed for the recent proof of the A 2 conjecture we prove a related pair of conjectures link...

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Bibliographic Details
Published inIntegral equations and operator theory Vol. 76; no. 3; pp. 421 - 446
Main Authors Cruz-Uribe, David, Moen, Kabe
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.07.2013
Subjects
Analysis
Mathematics
Mathematics and Statistics
two weight inequalities
42B35
42B25
42B30
sharp constants
fractional integral operators
Riesz potentials
bump conditions
Muckenhoupt weights
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Summary:In the 1970s Muckenhoupt and Wheeden made several conjectures relating two weight norm inequalities for the Hardy-Littlewood maximal operator to such inequalities for singular integrals. Using techniques developed for the recent proof of the A 2 conjecture we prove a related pair of conjectures linking the Riesz potential and the fractional maximal operator. As a consequence we are able to prove a number of sharp one and two weight norm inequalities for the Riesz potential.
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-013-2059-z