On the spaces Lp(x)(Ω) and Wm, p(x)(Ω)

In this paper we present some basic results on the generalized Lebesgue spaces L-p(x)(Omega) and generalized Lebesgue-Sobolev spaces W-m,W-p(x)(Omega). These results provide the necessary framework for the study of variational problems and elliptic equations with non-standard p(x)-growth conditions. (C) 2001 Academic Press.