Erhling's Inequality and Pseudo-Differential Operators on 𝐿ᵖ(IRᴺ)

Abstract

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