论文标题
有条件居中的时刻和紧凑型操作员在$ l^p $空间上的急剧估算
Sharp estimates for conditionally centred moments and for compact operators on $L^p$ spaces
论文作者
论文摘要
令$（ω，\ Mathcal {f}，\ Mathbf {p}）$为概率空间，$ξ$是$（ω，\ Mathcal {f}上的随机变量$ \ mathbf {e}^\ mathcal {g} = \ mathbf {e}（\ cdot | \ mathcal {g}）$是相应的条件期望运算符。我们在$ξ-\ Mathbf {e}^\ Mathcal {g}ξ$的矩时，以$ξ$的矩矩为单位上获得了清晰的估计。这使我们可以在$ l^p（[0，1]）$，$ 1 <p <\ infty $的有限紧凑型近似属性中找到最佳常数。
Let $(Ω, \mathcal{F}, \mathbf{P})$ be a probability space, $ξ$ be a random variable on $(Ω, \mathcal{F}, \mathbf{P})$, $\mathcal{G}$ be a sub-$σ$-algebra of $\mathcal{F}$, and let $\mathbf{E}^\mathcal{G} = \mathbf{ E}(\cdot | \mathcal{G})$ be the corresponding conditional expectation operator. We obtain sharp estimates for the moments of $ξ- \mathbf{E}^\mathcal{G}ξ$ in terms of the moments of $ξ$. This allows us to find the optimal constant in the bounded compact approximation property of $L^p([0, 1])$, $1 < p < \infty$.
