Mutually non isomorphic mixed-norm Lebesgue spaces

We prove that for $1\le p,q\le \mathrm{\infty }$ the mixed-norm spaces $L_q(L_p)$ are mutually non-isomorphic, with the only exception that $L_q(L_2)$ is isomorphic to $L_q(L_q)$ for all $1<q<\mathrm{\infty }$.