$A_\infty$ condition for general bases revisited: Complete classification of definitions
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- by Dariusz Kosz
- Proc. Amer. Math. Soc. 150 (2022), 3831-3839
- DOI: https://doi.org/10.1090/proc/16014
- Published electronically: May 27, 2022
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Abstract:
We refer to the discussion on different characterizations of the $A_\infty$ class of weights, initiated by Duoandikoetxea, Martín-Reyes, and Ombrosi [Math. Z. 282 (2016), pp. 955–972]. Twelve definitions of the $A_\infty$ condition are considered. For cubes in $\mathbb {R}^d$ every two conditions are known to be equivalent, while for general bases we have a trichotomy: equivalence, one-way implication, or no dependency may occur. In most cases the relations between different conditions have already been established. Here all the unsolved cases are treated and, as a result, a full diagram of the said relations is presented.References
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Bibliographic Information
- Dariusz Kosz
- Affiliation: Basque Center for Applied Mathematics, 48009 Bilbao, Spain; and Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, 50-370, Wrocław, Poland
- MR Author ID: 1129482
- Email: dariusz.kosz@pwr.edu.pl
- Received by editor(s): June 7, 2021
- Published electronically: May 27, 2022
- Additional Notes: The author was supported by the Basque Government through the BERC 2018-2021 program, by the Spanish State Research Agency through BCAM Severo Ochoa excellence accreditation SEV-2017-2018, and by the Foundation for Polish Science through the START Scholarship.
- Communicated by: Dmitriy Bilyk
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3831-3839
- MSC (2020): Primary 42B25
- DOI: https://doi.org/10.1090/proc/16014
- MathSciNet review: 4446233