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Integral Equations and Operator Theory

, Volume 76, Issue 3, pp 421–446 | Cite as

A Fractional Muckenhoupt–Wheeden Theorem and its Consequences

  • David Cruz-Uribe
  • SFO
  • Kabe MoenEmail author
Article

Abstract

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.

Mathematics Subject Classification (2010)

42B25 42B30 42B35 

Keywords

Riesz potentials fractional integral operators Muckenhoupt weights sharp constants two weight inequalities bump conditions 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsTrinity CollegeHartfordUSA
  2. 2.Department of MathematicsUniversity of AlabamaTuscaloosaUSA

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