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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 25, Issue 4


Characterizations of Besov and Triebel–Lizorkin spaces on metric measure spaces

Amiran Gogatishvili
  • Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Prague 1, Czech Republic
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/ Pekka Koskela / Yuan Zhou
  • Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China, and Department of Mathematics and Statistics, University of Jyväskylä, P. O. Box 35 (MaD), FI-40014, Finland
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Published Online: 2013-07-01 | DOI: https://doi.org/10.1515/form.2011.135


On a metric measure space satisfying the doubling property, we establish several optimal characterizations of Besov and Triebel–Lizorkin spaces, including a pointwise characterization. Moreover, we discuss their (non)triviality under a Poincaré inequality.

Keywords: Besov space; Triebel–Lizorkin space; Hajłasz–Besov space; Hajłasz–Triebel–Lizorkin space; metric measure space; sharp maximal function

About the article

Received: 2011-02-16

Revised: 2011-04-11

Published Online: 2013-07-01

Published in Print: 2013-07-01

Citation Information: Forum Mathematicum, Volume 25, Issue 4, Pages 787–819, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.135.

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