Vector valued Orlicz spaces generalized<i>N</i>-functions. I

Abstract

The theory of Orlicz spaces generated by JV-f unctions of a real variable is well known. On the other hand, as was pointed out by Wang, this same theory generated by ^-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 iV-functions (called GNfunctions) which are a natural generalization of the functions studied by Wang and the variable iV-functions by Portnov.