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Intrinsic characterizations of Besov spaces on Lipschitz domains
Author(s) -
Dispa Sophie
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310101
Subject(s) - mathematics , besov space , lipschitz continuity , characterization (materials science) , pure mathematics , equivalence (formal languages) , bounded function , norm (philosophy) , smoothness , interpolation space , mathematical analysis , functional analysis , biochemistry , materials science , political science , law , gene , nanotechnology , chemistry
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.