Author:
Arendt Wolfgang,Bu Shangquan
Abstract
AbstractLet $1\leq p,q\leq\infty$, $s\in\mathbb{R}$ and let $X$ be a Banach space. We show that the analogue of Marcinkiewicz’s Fourier multiplier theorem on $L^p(\mathbb{T})$ holds for the Besov space $B_{p,q}^s(\mathbb{T};X)$ if and only if $1\ltp\lt\infty$ and $X$ is a UMD-space. Introducing stronger conditions we obtain a periodic Fourier multiplier theorem which is valid without restriction on the indices or the space (which is analogous to Amann’s result (Math. Nachr.186 (1997), 5–56) on the real line). It is used to characterize maximal regularity of periodic Cauchy problems.AMS 2000 Mathematics subject classification: Primary 47D06; 42A45
Publisher
Cambridge University Press (CUP)
Cited by
113 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献