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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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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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 generalization Uchiyama’s construction of certain extremal BMO -functions and John-Nirenberg’s lemma.
AbstractList 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.
Author Kinnunen, Juha
Korte, Riikka
Shanmugalingam, Nageswari
Marola, Niko
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  surname: Shanmugalingam
  fullname: Shanmugalingam, Nageswari
  organization: Department of Mathematical Sciences, University of Cincinnati
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10.1215/S0012-7094-00-10238-4
10.1307/mmj/1029002851
10.1007/BF02788242
10.1007/BF02807405
10.2140/pjm.2001.201.289
10.1007/s11854-008-0047-z
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10.2140/pjm.1982.99.183
10.1512/iumj.2008.57.3168
10.2307/1971171
10.1512/iumj.1979.28.28037
10.1007/BFb0091154
10.14321/realanalexch.28.2.0649
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Issue 3
Keywords John–Nirenberg lemma
Bounded mean oscillation
Secondary 43A85
Analysis on metric measure spaces
Doubling condition
Primary 30L99
Language English
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Reimann (CR16) 1974; 49
Korte, Marola, Shanmugalingam (CR11) 2012; 50
Kronz (CR12) 2001; 106
Astala (CR1) 1983; 30
CR6
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CR18
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Strömberg (CR17) 1979; 28
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Kinnunen, Korte, Shanmugalingam, Tuominen (CR9) 2008; 57
Uchiyama (CR19) 1982; 99
Korte, Kansanen (CR10) 2011; 27
Maasalo (CR14) 2008; 106
Mateu, Mattila, Nicolau, Orobitg (CR15) 2000; 102
Gotoh (CR7) 2006; 97
Björn, Björn (CR2) 2011
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M Kronz (126_CR12) 2001; 106
SM Buckley (126_CR3) 1999; 79
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J-O Strömberg (126_CR17) 1979; 28
J Mateu (126_CR15) 2000; 102
J García-Cuerva (126_CR4) 1985
AK Lerner (126_CR13) 2002; 28
K Astala (126_CR1) 1983; 30
J Kinnunen (126_CR9) 2008; 57
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R Korte (126_CR11) 2012; 50
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Y Gotoh (126_CR8) 2001; 201
R Korte (126_CR10) 2011; 27
OE Maasalo (126_CR14) 2008; 106
A Björn (126_CR2) 2011
Y Gotoh (126_CR7) 2006; 97
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Snippet This paper studies functions of bounded mean oscillation ( BMO ) on metric spaces equipped with a doubling measure. The main result gives characterizations for...
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StartPage 405
SubjectTerms Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Title A characterization of BMO self-maps of a metric measure space
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