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New interpolation theorems are formulated for the class of operators that map the cone of positive functions into the cone of monotonic decreasing functions. These theorems are based on the concept of the Kc-functional. A formula for calculating the Kc-functional for some pairs of spaces is suggested. An example of an interpolation pair of spaces is considered in which the cones obtained with the help of Peetre's K-functional are different from those obtained using the Kc-functional.

This article is concerned with extension operators for the Sobolev spaces , where is a domain in with boundary in a Lipschitz class. Two-sided bounds are obtained for the minimum norm of an extension operator that are exact with respect to the smoothness parameter .