descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 22 Oct 2014Embargo end date: 01 Jan 2013 English Publisher:Springer Science and Business Media LLCJournal:Collectanea Mathematica, volume 66, pages 405-421 (issn: 0010-0757, eissn: 2038-4815,

Authors: Nageswari Shanmugalingam; Juha Kinnunen; Niko Marola; Riikka Korte;

doi: 10.1007/s13348-014-0126-7 , 10.48550/arxiv.1308.3933

arXiv: http://arxiv.org/abs/1308.3933

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

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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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Keywords

Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics

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