The quasinormed Neumann–Schatten ideals and embedding theorems for the generalized Lions–Peetre spaces of means

For the spaces $\varphi(X_0,X_1)_{p_0,p_1}$, which generalize the spaces of means introduced by Lions and Peetre to the case of functional parameters, necessary and sufficient conditions are found for embedding when all parameters (the function $\varphi$ and the numbers $1\leq p_0$, $p_1\leq\infty)$ vary. The proof involves a description of generalized Lions–Peetre spaces in terms of orbits and co-orbits of von Neumann–Schatten ideals (including quasinormed ideals).