We present a survey of recent applications of interpolation ideas in the study of sectorial operators.

In this paper we prove some interpolation inequalities between functions and their derivatives in the class of weighted Sobolev spaces defined on unbounded open subset Ω ⊂ Rn .

We extend recent results by Pisier on K-subcouples, i.e. subcouples of an interpolation couple that preserve the K-functional (up to constants) and corresponding notions for quotient couples. Examples include interpolation (in the pointwise sense) and a reinter-pretation of the Adamyan-Arov-Krein theorem for Hankel operators.