VECTOR VALUED ORLICZ SPACES GENERALIZED N-FUNCTIONS .I.

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 t define vector-valued Orlicz spaces and examine the resulting theory. © 1969 by Pacific Journal of Mathematics.