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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Additional Information
- Hans-Gerd Leopold
- Affiliation: Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich- Schiller-Universität Jena, D-07740 Jena, Germany
- Email: leopold@minet.uni-jena.de
- Elmar Schrohe
- Affiliation: Max-Planck-Arbeitsgruppe “Partielle Differentialgleichungen und Komplexe Ana- lysis”, Universität Potsdam, D-14415 Potsdam, Germany
- Email: schrohe@mpg-ana.uni-potsdam.de
- Received by editor(s): July 29, 1996
- Additional Notes: The first author was supported in part by DFG-contract Tr 374/1-1
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 3679-3687
- MSC (1991): Primary 35P05, 35H05, 47G30
- DOI: https://doi.org/10.1090/S0002-9939-97-04123-3
- MathSciNet review: 1423315