Type and Cotype of Musielak–Orlicz Sequence Spaces

Author： Horváth E.J.  

Publisher： Academic Press

ISSN： 0022-247X

Source： Journal of Mathematical Analysis and Applications, Vol.226, Iss.2, 1998-10, pp. : 431-455

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Abstract

Let &phis; = (&phis;n) be a Musielak–Orlicz function and l&phis; the Musielak–Orlicz sequence space generated by &phis;. It is shown that &phis; satisfies condition δq iff &phis; is equivalent to a q-concave function ψ = (ψn). It is also proved that l&phis; is of cotype q (type p) if and only if &phis; satisfies condition δq (δ2 and δ*p conditions, respectively). As applications we obtain characterization of the type and cotype of various sequence spaces: Nakano, weighted Orlicz, and Orlicz sequence spaces. Furthermore, a relation between q-concavity (p-convexity), lower q-estimate (upper p-estimate), and cotype (type) of l&phis; is given.

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