Singular convolution integrals with operator-valued kernel

被引：16
|
作者：
Hytonen, Tuomas
Weis, Lutz
机构：
[1] Univ Helsinki, Dept Math & Stat, FIN-00014 Helsinki, Finland
[2] Univ Karlsruhe, Inst Math 1, D-76128 Karlsruhe, Germany
来源：
MATHEMATISCHE ZEITSCHRIFT | 2007年 / 255卷 / 02期
关键词：
D O I：
10.1007/s00209-006-0043-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study operators f -> Kf of the form (Kf)(t) = integral(Rn)k(t-s)f(s) ds, where f is a vector-valued function and k an operator-valued singular kernel. Sufficient conditions for boundedness on L-p supercript stop-spaces of UMD-valued functions are given in terms of a Hormander-type condition involving R-boundedness. The results cover large classes of kernels and also provide new proofs of recent operator-valued Fourier multiplier theorems. Moreover, they give new information about families of singular integral operators.
引用
收藏
页码：393 / 425
页数：33
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