An imbedding theorem for Musielak-Sobolev spaces

Let Omega be a bounded domain in R-N and A epsilon C1-0 ((Omega) over bar x [0,+infinity)) be a Musielak-Orlicz function. We established an imbedding theorem for the Musielak-Sobolev space W-1,W-A(Omega) of the form W-1,W-A(Omega) hooked right arrow L-A* (Omega), where A(*) is the Sobolev conjugate function of A, a Musielak-Orlicz function defined in the paper. This theorem extends the imbedding theorem established by Donaldson and Trudinger for Orlicz-Sobolev spaces to the case of Musielak-Sobolev spaces. (C) 2011 Elsevier Ltd. All rights reserved.