Revista Matemática Iberoamericana

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Volume 27, Issue 1, 2011, pp. 335–354
DOI: 10.4171/RMI/638

Published online: 2011-04-30

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

Outi Elena Kansanen[1] and Riikka Korte[2]

(1) KTH, Stockholm, Sweden
(2) University of Helsinki, Finland

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.

Keywords: Metric doubling measure, metric spaces, Muckenhoupt weights, strong $A_\infty$-weight.

Kansanen Outi Elena, Korte Riikka: Strong $A_\infty$-weights are $A_\infty$-weights on metric spaces. Rev. Mat. Iberoamericana 27 (2011), 335-354. doi: 10.4171/RMI/638