Geodesic
On the Equivalence of Spectra of Linear Partial Differential Operators in Certain Function Spaces
Matematičeskie zametki, Tome 72 (2002) no. 6, pp. 909-917.

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For linear differential operators with coefficients of class $C$ on $\mathbb R^n$, we prove theorems on the simultaneous invertibility and equivalence of spectra in the Lebesgue space $L^p$, Stepanov space $M^p$, and in a particular Banach space $V^p\subset L^p$, $p\ge 1$. 
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V. M. Tyurin. On the Equivalence of Spectra of Linear Partial Differential Operators in Certain Function Spaces. Matematičeskie zametki, Tome 72 (2002) no. 6, pp. 909-917. http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a10/

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