Besov spaces on open sets
Besov spaces on open sets
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DOI：
10.1016/j.bulsci.2019.01.008
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发表时间：
2016-02
期刊：
影响因子：
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通讯作者：
T. Iwabuchi;T. Matsuyama;K. Taniguchi
中科院分区：
文献类型：
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作者：
T. Iwabuchi;T. Matsuyama;K. Taniguchi
利用Dirichlet边值条件下Schr dinger算子的谱定理，给出了Rn中任意开集Ω上Besov空间的定义.关键是在Ω上引入一些检验函数空间。给出了Besov空间的嵌入关系、对偶性等基本性质，并建立了函数正则性由Dirichlet Laplacian算子和Schr dinger算子度量的Besov空间之间的同构关系.
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set Ω of R n via the spectral theorem for the Schrödinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test function spaces on Ω. The fundamental properties of Besov spaces are also shown, such as embedding relations and duality, etc. Furthermore, the isomorphism relations are established among the Besov spaces in which regularity of functions is measured by the Dirichlet Laplacian and the Schrödinger operators.