Type and Cotype of Musielak]Orlicz Sequence Spaces*

Let f s fn. be a Musielak]Orlicz function and lf the Musielak]Orlicz sequence space generated by f. It is shown that f satisfies condition d q iff f is equivalent to a q-concave function c s cn.. It is also proved that lf is of cotype q type p.if and only if f satisfies conditiondq d2 and d *p conditions, respec- tively.. As applications we obtain characterization of the type and cotype of various sequence spaces: Nakano, weighted Orlicz, and Orlicz sequence spaces. Further- more, a relation between q-concavity p-convexity., lower q-estimate upper p- estimate., and cotype type. of lf is given