| SOME REMARKS ABOUT THE R-BOUNDEDNESS |
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| 引用本文： | BU Shangquan. SOME REMARKS ABOUT THE R-BOUNDEDNESS[J]. 数学年刊B辑(英文版), 2004, 25(3): 421-432 |
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| 作者姓名： | BU Shangquan |
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| 作者单位： | BU SHANGQUAN Department of Mathematical Sciences，Tsinghua University，Beijing 100084，China.E-mail: sbu@math.tsinghua.edu.cn |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No.10271064) and the Excel-lent Young Teachers Program of the Ministry of Education of China |
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| 摘 要： | Let X,Y be UMD-spaces that have property (α), 1< p< ∞ and let M be anR-bounded subset in L(X, Y). It is shown that {T(M_k)_(k∈z): M_k, k(M_(k l)-M_k) ∈M for k∈Z} is an R-bounded subset of L(L~p (0,2π; X), L~p(0,2π; Y)), where T(M_m)_(k∈zdenotes the L~p-multiplier given by the sequence (M_k)_(k∈z), This generalizes a resultof Venni [10]. The author uses this result to study the strongly L~p-well-posedness ofevolution equations with periodic boundary condition. Analogous results for operator-valued L~p-multipliers on R are also given.
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| 关 键 词： | 集合 子集 序列 边界条件 周期 算子 |
| 收稿时间： | 2008-10-02 |
SOME REMARKS ABOUT THE R-BOUNDEDNESS |
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| BU Shangquan. SOME REMARKS ABOUT THE R-BOUNDEDNESS[J]. Chinese Annals of Mathematics,Series B, 2004, 25(3): 421-432 |
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| Authors: | BU Shangquan |
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| Affiliation: | Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
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| Abstract: | Let X, Y be UMD-spaces that have property (α), I ＜ p ＜∞ and let M be an R-bounded subset in ( )(X,Y). It is shown that {T(Mk)k∈z : Mk,k(Mk+1 - Mk) ∈M for k ∈ Z} is an R-bounded subset of ( )(Lp(0, 2π; X), Lp(0, 2π; Y)), where T(Mk)k∈z denotes the Lp-multiplier given by the sequence (Mk)k∈z. This generalizes a result of Venni [10]. The author uses this result to study the strongly Lp-well-posedness of evolution equations with periodic boundary condition. Analogous results for operatorvalued Lp-multipliers on R are also given. |
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| Keywords: | Operator-valued Fourier multiplier Maximal regularity Rademacher boundedness |
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