Type and Cotype in Vector-Valued Nakano Sequence Spaces

Given a sequence of Banach spaces Xn4n and a sequence of real numbers pn4n in 1, ., the vector-valued Nakano sequence spaces lŽ pn4, Xn4. consist of ele- ments xn4n in Łn Xn for which there is a constant 0 such that ÝnŽ xn . pn . In this paper we find the conditions on the Banach spaces Xn and on the sequence pn4n for the spaces l Ž pn4, Xn4. to have cotype q or type p