In the Handbook of the Geometry of Banach Spaces, vol 1, page 855, Johnson and Schechtman say that if $M$ is an Orlicz function, the following are equivalent:

- The unit vector basis of the Orlicz space $\ell_M$ is $p$-convex and $2$-concave;
- $M(\left|t\right|^\frac{1}{p})$ is equivalent to a convex function and $M(t^{\frac{1}{2}})$ is equivalent to a concave function on $[0, \infty)$

And they give as reference *Application de l'étude de certaines formes linéaires aléatoires au plongement d'espaces de Banach dans des espaces $L^p$*, by J. Bretagnolle and D. Dacunha-Castelle, which I cannot understand since I don't speak French.

So my question is: how does one prove this result?

Thank you!