Abstract
AbstractThe aim of this paper is to study the equivalence between quasi‐norms of Besov spaces on domains. We suppose that the domain Ω ⊂ ℝn is a bounded Lipschitz open subset in ℝn. First, we define Besov spaces on Ω as the restrictions of the corresponding Besov spaces on ℝn. 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 ℝn described in Theorem 2.4 to the case of Lipschitz domains.
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