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Intrinsic characterizations of Besov spaces on Lipschitz domains

✍ Scribed by Sophie Dispa

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 196 KB
Volume: 260
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310101

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✦ Synopsis

Abstract

The aim of this paper is to study the equivalence between quasi‐norms of Besov spaces on domains. We suppose that the domain Ω ⊂ ℝ^n^ is a bounded Lipschitz open subset in ℝ^n^. First, we define Besov spaces on Ω as the restrictions of the corresponding Besov spaces on ℝ^n^. Then, with the help of equivalent and intrinsic characterizations (the Peetre‐type characterization 3.10 and the characterization via local means 3.13) of these spaces, we get another equivalent and intrinsic quasi‐norm using, this time, generalized differences and moduli of smoothness. We extend the well‐known characterization of Besov spaces on ℝ^n^ described in Theorem 2.4 to the case of Lipschitz domains.

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