On estimates of interpolation orbits

In this paper the orbits for some pairs of spaces are described in the case when the latter cannot be described by the $K$-method. A new estimate from below is given for the orbits of arbitrary pairs of spaces, and it is shown to be sharp. New examples of classical pairs of spaces are found for which the interpolation orbits are not described by the $K$-method, and an interpolation theorem for scales of spaces is proved, which cannot be obtained by the complex method or the method of means, nor even by a combination of both.
Bibliography: 9 titles.