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

• Autores: Juha Kinnunen , Riikka Korte, Niko Marola, Nageswari Shanmugalingam
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 66, Fasc. 3, 2015, págs. 405-421
• Idioma: inglés
• DOI: 10.1007/s13348-014-0126-7
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• Resumen

  • 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.