Let Φ be a generalized Young’s
function and LΦ the corresponding Orlicz space, on a general measure space. The
problem considered here is the characterization of the dual space (LΦ)∗, in terms
of integral representations, without any further restrictions. A complete
solution of the problem is presented in this paper. If Φ is continuous and the
measure space is sigma finite (or localizable), then a characterization of
the second dual (LΦ)∗∗ is also given. A detailed account of the quotient
spaces of LΦ relative to certain subspaces is presented; and the analysis
appears useful in the study of such spaces as the Riesz and Köthe-Toeplitz
spaces.
