Resumen de A characterization of {{\mathrm{BMO}}} self-maps of a metric measure space

Juha Kinnunen , Riikka Korte, Niko Marola, Nageswari Shanmugalingam

• This paper studies functions of bounded mean oscillation ({{\mathrm{BMO}}}) on metric spaces equipped with a doubling measure. The main result gives characterizations for mappings that preserve {{\mathrm{BMO}}}. This extends the corresponding Euclidean results by Gotoh to metric measure spaces. The argument is based on a generalization Uchiyama’s construction of certain extremal {{\mathrm{BMO}}}-functions and John-Nirenberg’s lemma.