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

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Abstract

We give a version of Erhling's inequality for Lp-Sobolev spaces Hs,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 Lp(IRn), 1 < p < âˆž. Applications to essential spectra of pseudo-differentials operators and strongly continuous one-parameter semigroups generated by pseudo-differential operators on Lp(IRn), 1 < p < âˆž, are given.  

Keywords

Erhling‘s inequality , Sobolev spaces , pseudo-differential operators , Agmon-Douglis-Nirenberg inequality , essential spectra , dissipative operators , semigroups
  • M. W. Wong Department of Mathematics and Statistics, York University 4700 Keelec Street, Toronto, Ontario M3J 1P3, Canada.
  • Pages: 97–108
  • Date Published: 2006-04-01
  • Vol. 8 No. 1 (2006): CUBO, A Mathematical Journal

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Published

2006-04-01

How to Cite

[1]
M. W. Wong, “Erhling’s Inequality and Pseudo-Differential Operators on 𝐿ᵖ(IRá´º)”, CUBO, vol. 8, no. 1, pp. 97–108, Apr. 2006.

Issue

Vol. 8 No. 1 (2006): CUBO, A Mathematical Journal

Section

Articles