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arXiv · 1211.5947

Interpolation of Ces{\`a}ro sequence and function spaces

Sergey V. Astashkin·Lech Maligranda
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Abstract

The interpolation property of Ces{\`a}ro sequence and function spaces is investigated. It is shown that $Ces_p(I)$ is an interpolation space between $Ces_{p_0}(I)$ and $Ces_{p_1}(I)$ 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 Ces{\`a}ro sequence spaces. On the other hand, $Ces_p[0, 1]$ is not an interpolation space between $Ces_1[0, 1]$ and $Ces_{\infty}[0, 1]$.

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Sergey V. Astashkin, Lech Maligranda. 2012-11-26. Interpolation of Ces{\`a}ro sequence and function spaces. https://arxiv.org/abs/1211.5947

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