Mixed-norm spaces H(p, q, a) are a family of spaces of analytic functions which generalize standard weighted Bergman spaces and, as a limit case, Hardy spaces. They were introduced by Flett, but some of their properties were deduced previously by Hardy and Littlewood. The possible inclusions between them are completely characterized, but the norms of these inclusions are unknown in general. These norms, in some cases, could be of interest for other fields of Mathematics as Mathematical Physics or Number Theory. In this talk, based on a joint work with D. Vukotic, we will show some conditions under which we are able to prove the contractivity of the inclusion (that is, when the norm of the inclusion operator is exactly 1).