Revista Matemática Iberoamericana

Strong $A_\infty$-weights are $A_\infty$-weights on metric spaces

Outi Elina Kansanen and Riikka Korte

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Abstract

We prove that every strong $A_\infty$-weight is a Muckenhoupt weight in Ahlfors-regular metric measure spaces that support a Poincaré inequality. We also explore the relations between various definitions for $A_\infty$-weights in this setting, since some of these characterizations are needed in the proof of the main result.

Article information

Source
Rev. Mat. Iberoamericana, Volume 27, Number 1 (2011), 335-354.

Dates
First available in Project Euclid: 4 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1296828837

Mathematical Reviews number (MathSciNet)
MR2815740

Zentralblatt MATH identifier
1223.42016

Subjects
Primary: 42B35: Function spaces arising in harmonic analysis

Keywords
metric doubling measure metric spaces Muckenhoupt weights strong $A_\infty$-weight

Citation

Korte, Riikka; Kansanen, Outi Elina. Strong $A_\infty$-weights are $A_\infty$-weights on metric spaces. Rev. Mat. Iberoamericana 27 (2011), no. 1, 335--354. https://projecteuclid.org/euclid.rmi/1296828837


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