Diameters of classes of smooth functions

We describe the weak asymptotic behaviour of diameters of $n$-th order of the unit ball of $W_p^l H^\omega (I^d)$ in $L_q(I^d)$, where $I=(0,1)$, in dependence on $n$. Namely we consider the Kolmogorov diameter, the Gel'fand diameter, the linear diameter, the Aleksandrov diameter and the entropy diameter.