Revista Matemática Iberoamericana

Translation averages of dyadic weights are not always good weights

Lesley A. Ward

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Abstract

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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 18, Number 2 (2002), 379-407.

Dates
First available in Project Euclid: 28 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1051544242

Mathematical Reviews number (MathSciNet)
MR1949833

Zentralblatt MATH identifier
1033.42018

Subjects
Primary: 42B35: Function spaces arising in harmonic analysis 42B25: Maximal functions, Littlewood-Paley theory

Keywords
Doubling measures dyadic weights $A_p$ weights reverse Hölder weights Muckenhoupt weights translation average

Citation

Ward, Lesley A. Translation averages of dyadic weights are not always good weights. Rev. Mat. Iberoamericana 18 (2002), no. 2, 379--407. https://projecteuclid.org/euclid.rmi/1051544242


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