Disjointly homogeneous rearrangement invariant spaces via interpolation

A Banach lattice E is called p-disjointly homogeneous  , 1≤p≤∞1≤p≤∞, when every sequence of pairwise disjoint normalized elements in E   has a subsequence equivalent to the unit vector basis of ℓpℓp. Employing methods from interpolation theory, we clarify which r.i. spaces on [0,1][0,1] are p  -disjointly homogeneous. In particular, for every 1