Weak A_\infty weights and weak Reverse Hölder property in a space of homogeneous type

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Anderson , T C , Hytönen , T & Tapiola , O 2017 , ' Weak A_\infty weights and weak Reverse Hölder property in a space of homogeneous type ' , Journal of Geometric Analysis , vol. 27 , no. 1 , pp. 95-119 . https://doi.org/10.1007/s12220-015-9675-6

Title: Weak A_\infty weights and weak Reverse Hölder property in a space of homogeneous type
Author: Anderson, Theresa C.; Hytönen, Tuomas; Tapiola, Olli
Other contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2017
Language: eng
Number of pages: 25
Belongs to series: Journal of Geometric Analysis
ISSN: 1050-6926
DOI: https://doi.org/10.1007/s12220-015-9675-6
URI: http://hdl.handle.net/10138/313152
Abstract: In the Euclidean setting, the Fujii-Wilson-type A(infinity) weights satisfy a reverse Holder inequality (RHI), but in spaces of homogeneous type the best-known result has been that A(infinity) weights satisfy only a weak reverse Holder inequality. In this paper, we complement the results of Hytonen, Perez and Rela and show that there exist both A(infinity) weights that do not satisfy an RHI and a genuinely weaker weight class that still satisfies a weak RHI. We also show that all the weights that satisfy a weak RHI have a self-improving property, but the self-improving property of the strong reverse Holder weights fails in a general space of homogeneous type. We prove most of these purely non-dyadic results using convenient dyadic systems and techniques.
Subject: 111 Mathematics
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