Invariance of the 𝐿_{𝑝} spectrum for hypoelliptic operators

Leopold, Hans-Gerd; Schrohe, Elmar

doi:10.1090/S0002-9939-97-04123-3

Invariance of the $L_p$ spectrum for hypoelliptic operators
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by Hans-Gerd Leopold and Elmar Schrohe PDF

Proc. Amer. Math. Soc. 125 (1997), 3679-3687 Request permission

Abstract:

We show that the spectra of the $L_p$-realizations for a class of hypoelliptic (pseudo-)

differential operators are independent of $p$ in an interval around $p=2$ depending on the growth properties of the symbol. For elliptic operators we obtain the classical boundedness interval of Fefferman; in the general case we obtain a smaller interval which is as large as one can possibly expect it to be.

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