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Littlewood–Paley decompositions and Besov spaces on Lie groups of polynomial growth

✍ Scribed by G. Furioli; C. Melzi; A. Veneruso

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 193 KB
Volume: 279
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200510409

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✦ Synopsis

Abstract

We introduce a Littlewood–Paley decomposition related to any sub‐Laplacian on a Lie group G of polynomial volume growth; this allows us to prove a Littlewood–Paley theorem in this general setting and to provide a dyadic characterization of Besov spaces B ^s,q^ ~p~ (G ), s ∈ ℝ, equivalent to the classical definition through the heat kernel. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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