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Domination of powers of subelliptic pseudo-differential operators

Domination of powers of subelliptic pseudo-differential operators Abstract This paper is concerned with domination relations between powers of subelliptic pseudo-differential operators. Take L 1 , L 2 two subelliptic second order pseudodifferential operators, where the subellipticity condition is expressed in terms of Sobolev norms related to a metric g and both L j are assumed to have nonnegative symbols a j . Denote by g σ the dual metric of g with respect to the symplectic structure on the phase space . It is shown that the operator inequality is equivalent to the condition where 0 < α ≤ β are given, provided that ε 2 (the subellipticity index of L 2 ) is ≥ 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

Domination of powers of subelliptic pseudo-differential operators

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Publisher
de Gruyter
Copyright
Copyright © 2010 by the
ISSN
1867-1152
eISSN
1869-6090
DOI
10.1515/apam.2010.009
Publisher site
See Article on Publisher Site

Abstract

Abstract This paper is concerned with domination relations between powers of subelliptic pseudo-differential operators. Take L 1 , L 2 two subelliptic second order pseudodifferential operators, where the subellipticity condition is expressed in terms of Sobolev norms related to a metric g and both L j are assumed to have nonnegative symbols a j . Denote by g σ the dual metric of g with respect to the symplectic structure on the phase space . It is shown that the operator inequality is equivalent to the condition where 0 < α ≤ β are given, provided that ε 2 (the subellipticity index of L 2 ) is ≥ 1.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Mar 1, 2010

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