Estimates for $L_p$-norms of simple partial fractions

We obtain estimates for $L_p$-norms of simple partial fractions in terms of their $L_r$-norms on limited and unlimited segments of the real axis for different $p>1$ and $r>1$ (S. M. Nikolskii type inequalities). We adduce examples and remarks about sharpness of these inequalities and sphere of their application.