Isomorphic classification of Lp,qLp,q-spaces

We prove that for all 1≤p,q<∞1≤p,q<∞, p≠qp≠q, p≠1p≠1, p≠2p≠2 and p=2p=2, q>2q>2 the Banach space lp,qlp,q does not isomorphically embed into the space Lp,q(0,1)Lp,q(0,1). We also prove under the same conditions that the space Lp,q(0,∞)Lp,q(0,∞) does not isomorphically embed into the space Lp,q(0,1)⊕lp,qLp,q(0,1)⊕lp,q.