ABSTRACT
HENRYK HUDZIK Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznan, Poland and Institute of Mathematics, University of Technology, ul. Piotrowo 3a, 60-965 Poznan, Poland. PAWEL KOLWICZ Institute of Mathematics, University of Technology, ul. Piotrowo 3a, 60-965 Poznan, Poland
It is known that, if 4> is an A-function vanishing only at zero, then Orlicz-Bochner space L<j>(/z,X) is P-convex iff both L<j>(/x) and X are P -convex and P-convexity shifts from X into L<j>(/i, X) with the same number n ([10]). In this paper these two as sumptions on <P will be omitted. Moreover, the number n under which L d > ( / x , X) become P —convex will be found constructively. It turns out that it is different in the case of finite and infinite non-atomic measure space. It will be proved also the extension to the case of Musielak-Orlicz function space of Bochner type.
