Interpolation of Cesàro sequence and function spaces

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The interpolation property of Cesàro sequence and function spaces is investigated. It is shown that Cesₚ(I) is an interpolation space between Cesₚ₀(I) and Cesₚ₁(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, Cesₚ[0, 1] is not an interpolation space between Ces₁[0, 1] and Ces∞[0, 1].