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

被引：6
|
作者：
Hytonen, Tuomas P. [1 ]
Weis, Lutz [2 ]
机构：
[1] Univ Helsinki, Dept Math & Stat, FI-00014 Helsinki, Finland
[2] Univ Karlsruhe, Math Inst, D-76128 Karlsruhe, Germany
来源：
ARCHIV DER MATHEMATIK | 2008年 / 90卷 / 01期
基金：
芬兰科学院;
关键词：
R-boundedness; Fourier multiplier; laplace operator; imaginary powers;
D O I：
10.1007/s00013-007-2303-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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 (alpha). We prove the necessity of (alpha) for a number of conclusions of this kind, complementing analogous results of G. Lancien in the product-space theory of Fourier multipliers and H-infinity-calculus.
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页码：44 / 52
页数：9
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