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

Amiran Gogatishvili; Pekka Koskela; Yuan Zhou

doi:10.1515/form.2011.135

Published by De Gruyter July 1, 2013

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

Amiran Gogatishvili , Pekka Koskela and Yuan Zhou

From the journal Forum Mathematicum

https://doi.org/10.1515/form.2011.135

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Abstract.

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

Received: 2011-02-16

Revised: 2011-04-11

Published Online: 2013-07-01

Published in Print: 2013-07-01

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

Abstract.

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