of Bochner
type is P-convex if and only if both spaces 
and 
are P-convex.
In particular, the Lebesgue-Bochner space 
is P-convex iff 
is
P-convex.
Full paper in PDF:
$%P. Kolwicz and R. Płuciennik, P-convexity of Musielak-Orlicz function spaces of Bochner type,
Rev. Mat. Complut. 11 (1998), no. 1, 43–57.
%$
It is proved that the Musielak-Orlicz function space of Bochner
type is P-convex if and only if both spaces and are P-convex.
In particular, the Lebesgue-Bochner space is P-convex iff is
P-convex.
1991 Mathematics Subject Classification: 46E30, 46E40, 46B20.