Exact descriptions of some K and E functionals

Exact formulas for the K functional of some quasi-Banach couples of the type (X, L-infinity) are obtained. In particular we can cover the cases when X = L-p,L-q (Lorentz spaces), 0 < p < infinity, l less than or equal to q less than or equal to infinity and X = M-phi (Marcinkiewicz spaces). We also describe the K functional of the pair (L-p/q,L-1, L-p,L-q), 1 less than or equal to q less than or equal to p < infinity. This generalizes the Nilsson-Peetre description of K(t,f,L-1,L-q), see [11]. An optimal slicing technique gives an exact description of the E functional of the pair (L-p/q, L-p,L-q). (C) 1997 Academic Press.