Littlewood–Paley Equivalence and Homogeneous Fourier Multipliers

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• 作者：Shuichi Sato
• 关键词：Littlewood–Paley functions ; Marcinkiewicz integrals ; Fourier multipliers ; Sobolev spaces
• 刊名：Integral Equations and Operator Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：87
• 期：1
• 页码：15-44
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis;
• 出版者：Springer International Publishing
• ISSN：1420-8989
• 卷排序：87

文摘

We consider certain Littlewood–Paley operators and prove characterization of some function spaces in terms of those operators. When treating weighted Lebesgue spaces, a generalization to weighted spaces will be made for Hörmander’s theorem on the invertibility of homogeneous Fourier multipliers. Also, applications to the theory of Sobolev spaces will be given.