Let 1≤p<q≤∞ and let T be a subadditive operator acting on
Lp and Lq. We prove that T is bounded on the Orlicz space
Lϕ, where ϕ−1(u)=u1/pρ(u1/q−1/p) for some concave
function ρ and ∥T∥Lϕ→Lϕ≤Cmax{∥T∥Lp→Lp,∥T∥Lq→Lq}. The interpolation constant C, in general, is
less than 4 and, in many cases, we can give much better estimates for C. In
particular, if p=1 and q=∞, then the classical Orlicz interpolation
theorem holds for subadditive operators with the interpolation constant C=1.
These results generalize our results for linear operators obtained in
\cite{KM01}