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

Andrei K. Lerner ¹   ; Kabe Moen ²

¹ Department of Mathematics Bar-Ilan University 52900 Ramat Gan, Israel
² Department of Mathematics University of Alabama Tuscaloosa, AL 35487-0350, U.S.A.

Studia Mathematica, Tome 219 (2013) no. 3, pp. 247-267

Résumé

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).

Détail

DOI : 10.4064/sm219-3-5

Keywords: establish several mixed p a infty bounds calder zygmund operators only involve supremum address cases infty part constant measured using exponential logarithmic definition using fujii wilson definition particular answer question first author provide answer logarithmic factor conjecture hyt nen lacey moreover example bounds logarithmic factors arbitrarily smaller previously known bounds supremum suprema