Interpolation of Cesaro sequence and function spaces

The interpolation properties of Cesaro sequence and function spaces are investigated. It is shown that Ces(p)(I) is an interpolation space between Ces(p0)(I) and Ces(p1)(I) for 1 < p(0) < p(1) <= infinity and 1/p = (1 - theta)/p(0) + theta/p(1) with 0 < theta < 1, where I = [0, infinity) or [0, 1]. The same result is true for Cesaro sequence spaces. On the other hand, Ces(p)[0, 1] is not an interpolation space between Ces(1)[0, 1] and Ces(infinity)[0, 1].