Abstract
The paper studies the interpolation properties of net spaces $$N_{p,q}(M)$$ , when $$M$$ is the set of dyadic cubes in $$\mathbb{R}^{n}$$ , and also when $$M$$ is the family of all cubes with parallel faces to the coordinate axes in $$\mathbb{R}^{n}$$ . It is shown that, in the case when $$M$$ is the set of dyadic cubes the scale of spaces is closed with respect to the real interpolation method. In the case, when $$M$$ is the set of all cubes with parallel faces to the coordinate axes, an analogue of the Marcinkiewicz–Calderon theorem on cones of non-negative functions is given.