We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderón-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.
- Calderón-Zygmund decomposition
- Doubling measure
- Good-λ inequality
- John-Nirenberg lemma