Almost Diagonal Operators and Atomic and Molecular Decompositions

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• 作者：Wen Yuan ; Winfried Sickel ; Dachun Yang
• 刊名：Lecture Notes in Mathematics
• 出版年：2010
• 出版时间：2010
• 年：2010
• 卷：2005
• 期：1
• 页码：49-64
• 全文大小：225.1 KB

文摘

In the first part of this chapter we shall show that under certain restrictions on the parameters our spaces A_{p, q}s, t(\mathbbRn)A_{p, q}^{s, \tau }({\mathbb{R}}^ n) allow characterizations by smooth molecules and smooth atoms. This opens the door to the discretization of our distribution spaces A_{p, q}s, t(\mathbbRn)A_{p, q}^{s, \tau }({\mathbb{R}}^n) . Afterwards, based on these discretizations, we are able to compare the classes A_{p, q}s, t(\mathbbRn)A_{p, q}^{s, \tau }({\mathbb{R}}^n) with the Besov-Morrey spaces Ns_pqu (\mathbbRn)\mathcal{N}^s_{pqu} (\mathbb{R}^n) (see item (xxv) in Sect. 1.3) and the Triebel-Lizorkin-Morrey spaces Es_pqu (\mathbbRn)\mathcal{E}^s_{pqu} (\mathbb{R}^n) (see item (xxv) in Sect. 1.3).