Intrinsic characterizations of Besov spaces on Lipschitz domains
Intrinsic characterizations of Besov spaces on Lipschitz domains
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Lipschitz 域上 Besov 空间的本质特征
DOI：
10.1002/mana.200310101
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发表时间：
2003
影响因子：
1
通讯作者：
S. Dispa
中科院分区：
文献类型：
--
作者：
S. Dispa
本文的目的是研究整环上Besov空间的拟范数之间的等价性。我们假设整环Ω <$$> n是Ω <$n中的有界Lipschitz开子集.首先，我们定义Ω上的Besov空间作为Ω n上相应Besov空间的限制。然后，借助于这些空间的等价和内在刻画（Peetre型刻画3.10和通过局部平均刻画3.13），我们得到了另一个等价和内在的拟范数，这次是使用广义差和光滑模。我们将定理2.4中描述的Besov空间的著名特征推广到Lipschitz域的情况。
The 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.