Open Access
September, 2011 Geometric-arithmetic averaging of dyadic weights
Jill Pipher , Lesley A. Ward , Xiao Xiao
Rev. Mat. Iberoamericana 27(3): 953-976 (September, 2011).


The theory of Muckenhoupt's weight functions arises in many areas of analysis, for example in connection with bounds for singular integrals and maximal functions on weighted spaces. We prove that a certain averaging process gives a method for constructing $A_p$ weights from a measurably varying family of dyadic $A_p$ weights. This averaging process is suggested by the relationship between the $A_p$ weight class and the space of functions of bounded mean oscillation. The same averaging process also constructs weights satisfying reverse Hölder ($RH_p$) conditions from families of dyadic $RH_p$ weights, and extends to the polydisc as well.


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Jill Pipher . Lesley A. Ward . Xiao Xiao . "Geometric-arithmetic averaging of dyadic weights." Rev. Mat. Iberoamericana 27 (3) 953 - 976, September, 2011.


Published: September, 2011
First available in Project Euclid: 9 August 2011

zbMATH: 1231.42022
MathSciNet: MR2895340

Primary: 42B35
Secondary: 42B25

Keywords: $A_p$ weights , bidisc , bounded mean oscillation , dyadic harmonic analysis , dyadic weights , Muckenhoupt weights , multiparameter harmonic analysis , polydisc , product weights , reverse Hölder weights

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.27 • No. 3 • September, 2011
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