Interpolation of Cesàro sequence and function spaces

Sergey V. Astashkin; Lech Maligranda

Studia Mathematica, Tome 215 (2013), p. 39-69 / Harvested from The Polish Digital Mathematics Library

Résumé

The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that $C e s_{p} (I)$ is an interpolation space between $C e s_{p ₀} (I)$ and $C e s_{p ₁} (I)$ for 1 < p₀ < p₁ ≤ ∞ and 1/p = (1 - θ)/p₀ + θ/p₁ with 0 < θ < 1, where I = [0,∞) or [0,1]. The same result is true for Cesàro sequence spaces. On the other hand, $C e s_{p} [0, 1]$ is not an interpolation space between Ces₁[0,1] and $C e s_{\infty} [0, 1]$ .

Publié le : 2013-01-01

Zbl 06172508

EUDML-ID : urn:eudml:doc:285675

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     title = {Interpolation of Ces\`aro sequence and function spaces},
     journal = {Studia Mathematica},
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     year = {2013},
     pages = {39-69},
     zbl = {06172508},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-1-4}
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Sergey V. Astashkin; Lech Maligranda. Interpolation of Cesàro sequence and function spaces. Studia Mathematica, Tome 215 (2013) pp. 39-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-1-4/