|
|
| |
| SOME REMARKS ABOUT THE R-BOUNDEDNESS |
| |
Citation： |
BU Shangquan.SOME REMARKS ABOUT THE R-BOUNDEDNESS[J].Chinese Annals of Mathematics B,2004,25(3):421~432 |
| Page view： 1156
Net amount： 823 |
Authors： |
BU Shangquan; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10271064) and the Excellent
Young Teachers Program of the Ministry of Education of China. |
|
|
| Abstract： |
Let $X, Y$ be UMD-spaces that have property ($\alpha$), $1 < p <
\infty$ and let $\cM$ be an $R$-bounded subset in $\cL(X, Y)$. It
is shown that $\{T_{(M_k)_{k\in\Z}}: M_k, k(M_{k+1}- M_k)\in \cM
\ {\rm for}\ k\in\Z\}$ is an $R$-bounded subset of $\cL(L^p(0,
2\pi; X),$ $ L^p(0, 2\pi; Y))$, where $T_{(M_k)_{k\in\Z}}$ denotes
the $L^p$-multiplier given by the sequence $(M_k)_{k\in\Z}$. This
generalizes a result of Venni \cite{Venni}. The author uses this
result to study the strongly $L^p$-well-posedness of evolution
equations with periodic boundary condition. Analogous results for
operator-valued $L^p$-multipliers on $\R$ are also given. |
Keywords： |
Operator-valued Fourier multiplier, Maximal regularity, Rademacher
boundedness |
Classification： |
42A45, 42C99, 46B20, 47D06 |
|
|
Download PDF Full-Text
|
|
|
|
