Embedding the weighted Sobolev space $W^l_p(\Omega;v)$ in the space $L_p(\Omega;\omega)$

Several conditions on the weight functions $v$ and $\omega$ are obtained that guarantee the embedding inequality
$$ \|u\|_{L_p(\Omega;\omega)}\leqslant C\biggl[\biggl(\int_\Omega|\nabla_lu|^p\biggr)^{1/p}+\biggl(\int_\Omega|u|^pv\biggr)^{1/p}\biggr], \qquad 1<p<n/l. $$
Classes of weights $\omega$ and $v$ in which these conditions are both necessary and sufficient are described.