Musielak–Orlicz Besov-type and Triebel–Lizorkin-type spaces

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• 作者：Dachun Yang (1)
  Wen Yuan (1)
  Ciqiang Zhuo (1)
  
• 关键词：Musielak–Orlicz function ; Besov space ; Triebel–Lizorkin space ; Atom ; Molecule ; Embedding ; Fourier multiplier ; Pseudo ; differential operator ; Primary 42B35 ; Secondary 46E35 ; 42B25 ; 42B15 ; 47G30
• 刊名：Revista Matem篓垄tica Complutense
• 出版年：2014
• 出版时间：January 2014
• 年：2014
• 卷：27
• 期：1
• 页码：93-157
• 全文大小：733 KB
• 作者单位：Dachun Yang (1)
  Wen Yuan (1)
  Ciqiang Zhuo (1)
  
  1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, People’s Republic of China
  
• ISSN：1988-2807

文摘

Let $s\in \mathbb{R },q\in (0,\infty ],\varphi _1,\varphi _2:\mathbb{R }^n\times [0,\infty )\rightarrow [0,\infty )$ be two Musielak–Orlicz functions that, on the space variable, belong to the Muckenhoupt class $\mathbb{A }_\infty (\mathbb{R }^n)$ uniformly on the time variable. In this paper, the authors introduce Musielak–Orlicz Besov-type spaces ${\dot{B}}_{\varphi _1,\varphi _2,q}^{s,\tau }(\mathbb{R }^n)$ and Musielak–Orlicz Triebel–Lizorkin-type spaces ${\dot{F}}_{\varphi _1,\varphi _2,q}^{s,\tau }(\mathbb{R }^n)$ , and establish their $\varphi $ -transform characterizations in the sense of Frazier and Jawerth. The embedding and lifting properties, characterizations via Peetre maximal functions, local means, Lusin area functions, smooth atomic and molecular decompositions of these spaces are also presented. As applications, the boundedness on these spaces of Fourier multipliers with symbols satisfying some generalized H?rmander condition are obtained. These spaces have wide generality, which unify Musielak–Orlicz Hardy spaces, unweighted and weighted Besov(-type) and Triebel–Lizorkin(-type) spaces as special cases.