Mixed $A_p$-$A_{\infty} $ estimates with one supremum
Volume 219 / 2013
Studia Mathematica 219 (2013), 247-267
MSC: 42B20, 42B25.
DOI: 10.4064/sm219-3-5
Abstract
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).
