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Interpolation of Cesàro sequence and function spaces. (English) Zbl 1357.46023
Summary: The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that \(\text{ Ces}_p(I)\) is an interpolation space between \(\text{ Ces}_{p_0}(I)\) and \(\text{ Ces}_{p_1}(I)\) 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, \(\text{ Ces}_p[0, 1]\) is not an interpolation space between \(\text{ Ces}_1[0, 1]\) and \(\text{ Ces}_{\infty }[0, 1]\).

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B70 Interpolation between normed linear spaces
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