Peetre K-functional

Summary

The Peetre K-functional $K(t, x)$ measures how well an element $x$ of a sum $X_0 + X_1$ of two Banach spaces splits into pieces in $X_0$ and $X_1$. The size of the second piece carries the weight $t$. It is the basic tool of the real method of interpolation spaces. In approximation theory it links smoothness to approximation, since for suitable pairs of spaces it is equivalent to a modulus of smoothness.