A characterization of the inclusions between mixed norm spaces

We consider the mixed norm spaces of Hardy type studied by Flett and others. We study some properties of these spaces related to mean and pointwise growth and complement some partial results by various authors by giving a complete characterization of the inclusion between $H(p,q,\alpha )$ and $H(u,v,\beta ),$ depending on the parameters $p,q,\alpha ,u,v$ and $\beta \mathrm{.}$