OPERATOR-VALUED FOURIER MULTIPLIERS ON PERIODIC BESOV SPACES AND APPLICATIONS
2004 ◽
Vol 47
(1)
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pp. 15-33
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Keyword(s):
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
2007 ◽
Vol 59
(6)
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pp. 1207-1222
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Keyword(s):
2004 ◽
Vol 77
(2)
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pp. 175-184
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Keyword(s):
Keyword(s):
1981 ◽
Vol 90
(1-2)
◽
pp. 63-70
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Keyword(s):
1987 ◽
Vol 17
(3)
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pp. 591-612
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2016 ◽
Vol 50
(1)
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pp. 109-137
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