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ISSN:
1435-5337
DOI:
10.1515/form.2011.135

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Forum Mathematicum

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Characterizations of Besov and TriebelLizorkin spaces on metric measure spaces

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1Institute of Mathematics, Academy of Sciences of the Czech Republic, itn 25, 115 67 Prague 1, Czech Republic.

2Department of Mathematics and Statistics, University of Jyvskyl, P. O. Box 35 (MaD), FI-40014, Finland.

3Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China.

Citation Information: Forum Mathematicum. Volume 0, Issue 0, Pages -–-, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/form.2011.135,

Publication History:
Received:
2011-02-16
Revised:
2011-04-11

Abstract

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

Keywords.: Besov space; TriebelLizorkin space; HajaszBesov space; HajaszTriebelLizorkin space; metric measure space; sharp maximal function

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