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This paper studies functions of bounded mean oscillation (BMO) on metricspaces equipped with a doubling measure. The main result givescharacterizations for mappings that preserve BMO. This extends thecorresponding Euclidean results by Gotoh to metric measure spaces. The argumentis based on a generalizations Uchiyama's construction of certain extremalBMO-functions and John-Nirenberg's lemma.

A characterization of BMO self-maps of a metric measure space