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arXiv · 1308.3933

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

Juha Kinnunen·Riikka Korte·Niko Marola·Nageswari Shanmugalingam
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Abstract

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

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Juha Kinnunen, Riikka Korte, Niko Marola, Nageswari Shanmugalingam. 2015-10-01. A characterization of BMO self-maps of a metric measure space. https://doi.org/10.1007/s13348-014-0126-7

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