Extensions of theorems of Gagliardo and Marcus and Mizel to Orlicz spaces

In 1958, Gagliardo showed that if u is a locally integrable function on a domain Ω satisfying the cone condition, with all weak derivatives belonging to the Lebesgue space L (Ω) (1 ≤ p < ∞), then u belongs to L (Ω) also. We extend this result to Orlicz spaces, and use it to extend a result of Marcus and Mizel on Nemitsky operators between Sobolev spaces to Orlicz-Sobolev spaces