A generalized version of Holmstedt's formula for the K-functional

Abstract

Let $(A_0,A_1)$ be a compatible couple of quasi-normed spaces, and let $\hat{I}{¦}_0$ and $\hat{I}{¦}_1$ be two general parameters of $K$-interpolation method. We compute $K$-functional for the couple $((A_0,A_1{)}_{\hat{I}{¦}_0},(A_0,A_1{)}_{\hat{I}{¦}_1})$ in terms of $K$-functional for the couple $(A_0,A_1)$.