We prove that every strong -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 -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 -weights are -weights on metric spaces. Rev. Mat. Iberoam. 27 (2011), no. 1, pp. 335–354DOI 10.4171/RMI/638