Interpolation of Cesàro sequence and function spaces
Volume 215 / 2013
Studia Mathematica 215 (2013), 39-69
MSC: Primary 46E30, 46B70; Secondary 46B20.
DOI: 10.4064/sm215-1-4
Abstract
The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that ${\rm Ces}_p(I)$ is an interpolation space between ${\rm Ces}_{p_0}(I)$ and ${\rm Ces}_{p_1}(I)$ for $1 < p_0 < p_1 \leq \infty $ and $1/p = (1 - \theta )/p_0 + \theta /p_1$ with $0 < \theta < 1$, where $I = [0, \infty )$ or $[0, 1]$. The same result is true for Cesàro sequence spaces. On the other hand, ${\rm Ces}_p[0, 1]$ is not an interpolation space between ${\rm Ces}_1[0, 1]$ and ${\rm Ces}_{\infty }[0, 1]$.
