The theory of Orlicz spaces
generated by N-functions of a real variable is well known. On the other hand, as was
pointed out by Wang, this same theory generated by N-functions of more than one
real variable has not been discussed in the literature. The purpose of this paper is to
develop and study such a class of generalized N-functions (called GN-functions)
which are a natural generalization of the functions studied by Wang and the
variable N-functions by Portnov. In second part of this study we will utilize
GN-functions to define vector-valued Orlicz spaces and examine the resulting
theory.
