Fourier multipliers in Banach function spaces with UMD concavifications
Fourier multipliers in Banach function spaces with UMD concavifications
复制标题
具有 UMD 凹面的 Banach 函数空间中的傅立叶乘子
DOI：
--
复制
发表时间：
2017
影响因子：
1.3
通讯作者：
M. Veraar
中科院分区：
文献类型：
--
作者：
Alex Amenta;E. Lorist;M. Veraar
证明了Coifman-Rubio de Francia-Semmes乘子定理在Banach函数空间上对算子值乘子的各种推广。我们的结果涉及到一个新的算子集的有界性条件，我们称之为
ℓ
R
(
ℓ
S
)
{ell^{r}(ell^{S})}
-有界性，这意味着
R
数学{R}
-在许多情况下是有界的。这些证明是基于作者最近在Banach函数空间中得到的新的Littlewood-Paley-Rubio de Francia型估计。
We prove various extensions of the Coifman–Rubio de Francia–Semmes multiplier theorem to operator-valued multipliers on Banach function spaces. Our results involve a new boundedness condition on sets of operators which we call
ℓ
r
(
ℓ
s
)
{ell ^{r}(ell ^{s})}
-boundedness, which implies
R
mathcal {R}
-boundedness in many cases. The proofs are based on new Littlewood–Paley–Rubio de Francia-type estimates in Banach function spaces which were recently obtained by the authors.