On the power order of growth of lower $Q$-homeomorphisms

In the present paper we investigate the asymptotic behavior of $Q$-homeomorphisms with respect to a $p$-modulus at a point. The sufficient conditions on $Q$ under which a mapping has a certain order of growth are obtained. We also give some applications of these results to Orlicz–Sobolev classes $W^{1,\varphi}_{\mathrm{loc}}$ in $\mathbb{R}^n$, $n\geqslant 3$, under conditions of the Calderon type on $\varphi$ and, in particular, to Sobolev classes $W_{\mathrm{loc}}^{1,p},$ $p>n-1$. We give also an example of a homeomorphism demonstrating that the established order of growth is precise.