Mixed $A_{p}-A_{∞}$ estimates with one supremum

• Autorzy: Andrei K. Lerner , Kabe Moen
• Języki publikacji: EN

Abstrakty

EN

We establish several mixed $A_{p}-A_{∞}$ bounds for Calderón-Zygmund operators that only involve one supremum. We address both cases when the $A_{∞}$ 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).

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 219
• Numer: 3
• Strony: 247-267

Daty

wydano

2013

Twórcy

autor

Andrei K. Lerner

• Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel

autor

Kabe Moen

• Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A.

Identyfikatory

DOI

10.4064/sm219-3-5