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

Riikka Korte; Outi Elena Kansanen

doi:10.4171/rmi/638

JournalsrmiVol. 27, No. 1pp. 335–354

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

Riikka Korte
University of Helsinki, Finland
Outi Elena Kansanen
KTH, Stockholm, Sweden

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

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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.

Cite this article

Riikka Korte, Outi Elena Kansanen, Strong $A_{\infty}$ -weights are $A_{\infty}$ -weights on metric spaces. Rev. Mat. Iberoam. 27 (2011), no. 1, pp. 335–354

DOI 10.4171/RMI/638