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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Invariance of the ${L_p}$ Spectrum
for Hypoelliptic Operators


Authors: Hans-Gerd Leopold and Elmar Schrohe
Journal: Proc. Amer. Math. Soc. 125 (1997), 3679-3687
MSC (1991): Primary 35P05, 35H05, 47G30
MathSciNet review: 1423315
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04123-3
PII: S 0002-9939(97)04123-3
Keywords: $L_p$-spectrum, spectral independence, hypoelliptic pseudodifferential operators
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
Article copyright: © Copyright 1997 American Mathematical Society