Interpolation of Ces{à}ro sequence and function spaces

Abstract

The interpolation property of Ces{à}ro sequence and function spaces is investigated. It is shown that $Ce{s}_p(I)$ is an interpolation space between $Ce{s}_{p_0}(I)$ and $Ce{s}_{p_1}(I)$ for $1<p_0<p_1\le \infty$ 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 Ces{à}ro sequence spaces. On the other hand, $Ce{s}_p[0,1]$ is not an interpolation space between $Ce{s}_1[0,1]$ and $Ce{s}_{\infty }[0,1]$.

28 pages

Cited by in corpus (1)

• Hardy's operator and normability of generalized Lorentz-Marcinkiewicz spaces, with sharp or weakly sharp constant estimation