Revista Matemática Iberoamericana
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Published online: 2011-04-30
Strong $A_\infty$-weights are $A_\infty$-weights on metric spacesOuti Elena Kansanen and Riikka Korte (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. Iberoam. 27 (2011), 335-354. doi: 10.4171/RMI/638