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.
@article{1614,
title = {Erhling's Inequality and Pseudo-Differential Operators on L(IR)},
journal = {CUBO, A Mathematical Journal},
volume = {8},
year = {2006},
language = {en},
url = {http://dml.mathdoc.fr/item/1614}
}
Wong, M. W. Erhling's Inequality and Pseudo-Differential Operators on 𝐿ᵖ(IRᴺ). CUBO, A Mathematical Journal, Tome 8 (2006) . http://gdmltest.u-ga.fr/item/1614/