The Function $G_\lambda^*$ as the Norm of a Calderón–Zygmund Operator

We describe a new approach to one of the quadratic functions in the Littlewood–Paley theory, namely, to the function $G_\lambda^*$. It is shown that some of its properties can be obtained from the general theory of operators of Calderón–Zygmund type (which, apparently, has not been considered applicable in this context). There are applications to interpolation theory.