Open Access
June, 2002 Translation averages of dyadic weights are not always good weights
Lesley A. Ward
Rev. Mat. Iberoamericana 18(2): 379-407 (June, 2002).


The process of translation averaging is known to improve dyadic BMO to the space BMO of functions of bounded mean oscillation, in the sense that the translation average of a family of dyadic BMO functions is necessarily a BMO function. The present work investigates the effect of translation averaging in other dyadic settings. We show that translation averages of dyadic doubling measures need not be doubling measures, translation averages of dyadic Muckenhoupt weights need not be Muckenhoupt weights, and translation averages of dyadic reverse Hölder weights need not be reverse Hölder weights. All three results are proved using the same construction.


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Lesley A. Ward. "Translation averages of dyadic weights are not always good weights." Rev. Mat. Iberoamericana 18 (2) 379 - 407, June, 2002.


Published: June, 2002
First available in Project Euclid: 28 April 2003

zbMATH: 1033.42018
MathSciNet: MR1949833

Primary: 42B25 , 42B35

Keywords: $A_p$ weights , doubling measures , dyadic weights , Muckenhoupt weights , reverse Hölder weights , translation average

Rights: Copyright © 2002 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.18 • No. 2 • June, 2002
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