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

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...

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Bibliographic Details
Published inCollectanea mathematica (Barcelona) Vol. 66; no. 3; pp. 405 - 421
Main Authors Kinnunen, Juha, Korte, Riikka, Marola, Niko, Shanmugalingam, Nageswari
Format Journal Article
LanguageEnglish
Published Milan Springer Milan 18.09.2015
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
John–Nirenberg lemma
Bounded mean oscillation
Secondary 43A85
Analysis on metric measure spaces
Doubling condition
Primary 30L99
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Summary: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 generalization Uchiyama’s construction of certain extremal BMO -functions and John-Nirenberg’s lemma.
ISSN:0010-0757
2038-4815
DOI:10.1007/s13348-014-0126-7