Median-Type John–Nirenberg Space in Metric Measure Spaces

Abstract We study the so-called John–Nirenberg space that is a generalization of functions bounded mean oscillation in setting metric measure spaces with doubling measure. Our main results are local and global inequalities, which give weak-type estimates for function. consider medians instead integral averages throughout, thus not priori assumed to be locally integrable. arguments based on Calderón–Zygmund decomposition good- $$\lambda $$ λ inequality medians. A up boundary proven by using chaining arguments. As consequence, integral-type median-type coincide under Boman-type assumption.