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

Andrei K. Lerner, and Kabe Moen. "Mixed $A_{p}-A_{∞}$ estimates with one supremum." Studia Mathematica 219.3 (2013): 247-267. <http://eudml.org/doc/285779>.

@article{AndreiK2013,
abstract = {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).},
author = {Andrei K. Lerner, Kabe Moen},
journal = {Studia Mathematica},
keywords = {Calderón-Zygmund operators; sharp weighted inequalities; -weights; -weights},
language = {eng},
number = {3},
pages = {247-267},
title = {Mixed $A_\{p\}-A_\{∞\}$ estimates with one supremum},
url = {http://eudml.org/doc/285779},
volume = {219},
year = {2013},
}

TY - JOUR
AU - Andrei K. Lerner
AU - Kabe Moen
TI - Mixed $A_{p}-A_{∞}$ estimates with one supremum
JO - Studia Mathematica
PY - 2013
VL - 219
IS - 3
SP - 247
EP - 267
AB - 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).
LA - eng
KW - Calderón-Zygmund operators; sharp weighted inequalities; -weights; -weights
UR - http://eudml.org/doc/285779
ER -