It is proved that the Musielak-Orlicz function space LF(mu,X) of Bochner type is P-convex if and only if both spaces LF(mu,R) and X are P-convex. In particular, the Lebesgue-Bochner space Lp(mu,X) is P-convex iff X is P-convex.
@article{urn:eudml:doc:44481, title = {P-convexity of Musielak-Orlicz function spaces of Bochner type.}, journal = {Revista Matem\'atica de la Universidad Complutense de Madrid}, volume = {11}, year = {1998}, pages = {43-57}, zbl = {0916.46021}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44481} }
Kolwicz, Pawel.; Pluciennik, Ryszard. P-convexity of Musielak-Orlicz function spaces of Bochner type.. Revista Matemática de la Universidad Complutense de Madrid, Tome 11 (1998) pp. 43-57. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44481/