On the necessity of property (α) for some vector-valued multiplier theorems

被引：0
|
作者：
Tuomas P. Hytönen
Lutz Weis
机构：
[1] University of Helsinki,Department of Mathematiscs and Statistics
[2] Universität Karlsruhe,Mathematisches Institut I
来源：
Archiv der Mathematik | 2008年 / 90卷
关键词：
Primary 42A45; Secondary 46B09; -boundedness; Fourier multiplier; Laplace operator; imaginary powers;
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摘要：
The notion of R-bounded operator families has proven to be crucial to several aspects of vector-valued Harmonic Analysis and its applications to PDEs. Concrete and important R-bounded sets have been identified among operators acting on UMD Banach spaces, which in addition enjoy G. Pisier’s property (α). We prove the necessity of (α) for a number of conclusions of this kind, complementing analogous results of G. Lancien in the product-space theory of Fourier multipliers and H∞-calculus.
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页码：44 / 52
页数：8
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