We give a version of Erhling's inequality for Lp-Sobolev spaces Hs,p on IRn, -∞ < s < ∞, 1 ≤ p < ∞ , and use it to establish an analogue of the Agmon Douglis-Nirenberg inequality for pseudo-differential operators perturbed by singular potentials on Lp(IRn), 1 < p < ∞. Applications to essential spectra of pseudo-differentials operators and strongly continuous one-parameter semigroups generated by pseudo-differential operators on Lp(IRn), 1 < p < ∞, are given.