On the p-convexity of Orlicz spaces (Q1071265)

Given \(0<p\leq 1\), we obtain some conditions in terms of the Orlicz function \(\Phi\) for the non p-convexity of the Orlicz spaces \(L^{\Phi}_{\Omega}\) on arbitrary measure spaces. The results are obtained using the galb theory of \textit{Ph. Turpin} [Diss. Math., Warszawa 131, 221 p. (1976; Zbl 0331.46001)] and they extend some results of \textit{W. Matuszewska} and \textit{W. Orlicz} [Stud. Math. 21, 107-115 (1961; Zbl 0202.399)] given for atomless finite measures.