论文标题
Volterra型积分操作员在单位球耐火空间上的刚性
Rigidity of Volterra-type integral operators on Hardy spaces of the unit ball
论文作者
论文摘要
我们确定在Hardy空间上的Volterra型积分运算符$ J_B $ $ h^p $的单位球$ \ Mathbb {B} _n $表现出相当强烈的刚性行为。更确切地说，我们表明，$ j_b $的紧凑性，严格的奇异性和$ \ ell^p $ - singularity等于$ h^p $，对于任何$ 1 \ le P <\ f \ infty $。此外，我们表明运算符$ j_b $作用于$ h^p $无法修复$ \ ell^2 $的同构副本。
We establish that the Volterra-type integral operator $J_b$ on the Hardy spaces $H^p$ of the unit ball $\mathbb{B}_n$ exhibits a rather strong rigid behavior. More precisely, we show that the compactness, strict singularity and $\ell^p$-singularity of $J_b$ are equivalent on $H^p$ for any $1 \le p < \infty$. Moreover, we show that the operator $J_b$ acting on $H^p$ cannot fix an isomorphic copy of $\ell^2$ when $p \ne 2.$
