论文标题
关于使用功能参数的真实插值的狮子彼得方法的稳定性
On the stability of the Lions-Peetre method of real interpolation with functional parameter
论文作者
论文摘要
令$ \ vec {x} =（x_0，x_1）$为兼容的班克空间，$ 1 \ le p \ le p \ le \ infty $，让$φ$为正质量concave函数。用$ \ Overline {x} _ {φ，p} =（x_0，x_1）_ {φ，p} $由S. Janson（1981）定义的真实插值空间。我们提供了$φ_{0} $，$φ_{1} $的必要条件 \ left（\ + edline {x} _ {φ_{0}，1}，\ edimelline {x} _ {φ_{1}，1} \ right）_ {φ，p} = \ left（\ edline {x} _ {φ_{0}，\ infty}，\ overline {x} _ {φ_{1}，\ infty}，\ infty}，\ right）所有BANACH夫妇$ \ Overline {x}。 $
Let $\vec{X}=(X_0, X_1)$ be a compatible couple of Banach spaces, $ 1\le p \le \infty$ and let $ φ$ be positive quasi-concave function. Denote by $\overline{X}_{φ,p}=(X_0,X_1)_{φ,p}$ the real interpolation spaces defined by S. Janson (1981). We give necessary and sufficient conditions on $ φ_{0}$, $φ_{1}$ and $φ$ for the validity of \begin{equation*} \left(\overline{X}_{φ_{0},1},\overline{X}_{φ_{1},1} \right) _{φ,p}= \left(\overline{X}_{φ_{0},\infty},\overline{X}_{φ_{1},\infty}\right)_{φ,p} \end{equation*} for all $ 1\le p\le \infty$, and all Banach couples $\overline{X}. $
