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Strong $$A_\infty$$-weights are $$A_\infty$$-weights on metric spaces. (English) Zbl 1223.42016
The authors study very interesting properties of the strong $$A_\infty$$-weights in an Ahlfors-regular metric space supporting a Poincaré inequality. They explore relations among various definitions of $$A_\infty$$-weights in the setting of metric spaces. Some definitions are equivalent to each other and others are not; counterexamples are given. Many of the results are shown, using proofs that are different from their Euclidean analogue.

##### MSC:
 42B35 Function spaces arising in harmonic analysis
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##### References:
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