On a Peetre functional

The Peetre $K$-functional is often used to describe and study the interpolation spaces associated with the real variable method. In the paper a modification of this functional, the Peetre $K_2$-functional
$$K_2(t,\mathbf x)=\inf_{\mathbf x=\mathbf x_1+\mathbf x_2}\sqrt{\|\mathbf x_1\|_1^2+t^2\|\mathbf x_2\|_2^2}$$
is treated as a function of $t$ for fixed $\mathbf x$, and its properties are studied. Several particular cases are considered and classes of functions expressible as $K_2(t)$ are investigated.