We study a class of spaces, $$JN_p$$ , related to $${{\mathrm{BMO}}}$$ in the abstract setting of a metric space with a doubling measure. We obtain a Reimann–Rychener type local to global result and also show that a Boman type condition is sufficient to make the embedding of $$JN_p$$ into weak $$L^{p}$$ to hold. We discuss certain necessary condition. Our abstract setting covers various situations at once and, in particular, includes all geodesic spaces.