Vol. 28, No. 1, 1969

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Vector valued Orlicz spaces generalized N-functions. I

Michael Samuel Skaff

Vol. 28 (1969), No. 1, 193–206

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.

Mathematical Subject Classification 2000
Primary: 46E40
Secondary: 46E30
Received: 10 July 1968
Published: 1 January 1969
Michael Samuel Skaff