Criteria for embedding of spaces constructed by the method of means with arbitrary quasi-concave functional parameters

We consider a generalization ϕ(X0,X1)p0,p1 of the method of means to arbitrary non-degenerate functional parameter. In this case non-trivial embedding ϕ(X0,X1)p0,p1⊂ψ(X0,X1)q0,q1 take place. We find necessary and sufficient condition for such embedding if 1⩽q0⩽p0⩽∞ and 1⩽q1⩽p1⩽∞ or 1⩽p0⩽q0⩽∞ and 1⩽p1⩽q1⩽∞.