Imbedding theorems for the spaces $H_p^{\omega,k}$ and $H_p^{s,\omega,k}$

Imbedding theorems for the spaces $H_p^{\omega,k}$ and $H_p^{s,\omega,k}$, $1<p<+\infty$ (with arbitrary smoothness function $\omega$) are studied. In particular, symmetric hulls of these spaces are described, necessary and sufficient conditions of imbedding in Orlicz and Lorentz spaces are derived, and unimprovable bounds of the moduli of continuity in $L_q$, $p<q\leq\infty$, are given.