Calculus of Variations and Geometric Measure Theory

J. Kinnunen - R. Korte - N. Marola - N. Shanmugalingam

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

created by marola on 19 Aug 2013
modified by shanmugal on 24 Jul 2015


To appear

Inserted: 19 aug 2013
Last Updated: 24 jul 2015

Journal: Collect. Math.
Year: 2015


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.