Hp -Maximal Regularity and Operator Valued Multipliers on Hardy Spaces
Hp -Maximal Regularity and Operator Valued Multipliers on Hardy Spaces
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Hp - Hardy 空间上的最大正则性和算子值乘数
DOI：
10.4153/cjm-2007-051-5
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
C. Merdy
中科院分区：
文献类型：
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作者：
Shangquan Bu;C. Merdy
摘要我们考虑柯西问题${u}^{\Prime}}(T)+au(T)=f(T)(t\，\in\mathbb{R})$在${H}^{p}}$意义下的极大正则性，其中$A$是Banach空间$X$上的闭算子，$f$是定义在$\mathbb{R}$上的$X$值函数。证明了：如果$X$是AUMD Banach空间，则$A$满足${H}^{p}$-极大正则性当且仅当$A$是$<；\FRAC{\pi}{2}型的Rademacher扇图。此外，我们还找到了一个算子$A$具有${H}^{p}$-极大正则性，它不具有经典的${L}^{p}}$-极大正则性。当$X$是AUMD Banach空间时，我们证明了Hardy空间${H}^{p}(\mathbb{R}；\，X)$上算子值傅立叶乘子的一个相关的Mikhlin型定理.
Abstract We consider maximal regularity in the ${{H}^{p}}$ sense for the Cauchy problem ${{u}^{\prime }}(t)+Au(t)=f(t)(t\,\in \mathbb{R})$ , where $A$ is a closed operator on a Banach space $X$ and $f$ is an $X$ -valued function defined on $\mathbb{R}$ . We prove that if $X$ is an AUMD Banach space, then $A$ satisfies ${{H}^{p}}$ -maximal regularity if and only if $A$ is Rademacher sectorial of type $<\frac{\pi }{2}.$ Moreover we find an operator $A$ with ${{H}^{p}}$ -maximal regularity that does not have the classical ${{L}^{p}}$ -maximal regularity. We prove a related Mikhlin type theorem for operator valued Fourier multipliers on Hardy spaces ${{H}^{p}}(\mathbb{R};\,X)$ , in the case when $X$ is an AUMD Banach space.