Orlicz functions that do not satisfy the ${\Delta }_2$-condition and high order Gateaux smoothness in $h_M(\Gamma )$

Milen Ivanov, Stanimir Troyanski, Nadia Zlateva

We study Orlicz functions that do not satisfy the ${\Delta }_2$-condition at zero. We prove that for every Orlicz function $M$ such that ${\mathrm{limsup}}_{t\to 0}M(t)/t^p>0$ for some $p\ge 1$, ther…