Mixed $A_p$-$A_{\infty} $ estimates with one supremum

Tom 219 / 2013

Andrei K. Lerner, Kabe Moen Studia Mathematica 219 (2013), 247-267 MSC: 42B20, 42B25. DOI: 10.4064/sm219-3-5


We establish several mixed $A_p$-$A_\infty $ bounds for Calderón–Zygmund operators that only involve one supremum. We address both cases when the $A_\infty $ part of the constant is measured using the exponential-logarithmic definition and using the Fujii–Wilson definition. In particular, we answer a question of the first author and provide an answer, up to a logarithmic factor, to a conjecture of Hytönen and Lacey. Moreover, we give an example to show that our bounds with the logarithmic factors can be arbitrarily smaller than the previously known bounds (both with one supremum and two suprema).


  • Andrei K. LernerDepartment of Mathematics
    Bar-Ilan University
    52900 Ramat Gan, Israel
  • Kabe MoenDepartment of Mathematics
    University of Alabama
    Tuscaloosa, AL 35487-0350, U.S.A.

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