The determination of the
function spaces X which are intermediate in the weak sense between Lp and Lq has
been shown, by the author, to depend on a pair of numbers (α,β) called the indices
of the space. The indices depend on the function norm of X and on the
properties of the underlying measure space: whether it has finite or infinite
measure, is non-atomic or atomic. In this paper, formulas are given for the
indices of an Orlicz space in case the measure space is non-atomic with finite
or infinite measure, or else is purely atomic with atoms of equal measure.
The indices for an Orlicz space over a non-atomic finite measure space turn
out to be the reciprocals of the exponents of the space as introduced by
Matuszewska and Orlicz, and generalized by Shimogaki. Some new results
concerning submultiplicative functions are used in the proof of the main
result.
