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Domination of powers of subelliptic pseudo-differential operators
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Sami Mustapha
Published/Copyright:
March 18, 2010
Abstract
This paper is concerned with domination relations between powers of subelliptic pseudo-differential operators. Take L1, L2 two subelliptic second order pseudodifferential operators, where the subellipticity condition is expressed in terms of Sobolev norms related to a metric g and both Lj are assumed to have nonnegative symbols aj. Denote by gσ 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 ε2 (the subellipticity index of L2) is ≥ 1.
Received: 2008-04-18
Revised: 2009-02-04
Published Online: 2010-03-18
Published in Print: 2010-March
© de Gruyter 2010
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Articles in the same Issue
- Schwarzian derivative and Numata Finsler structures
- Bi-Hamiltonian nature of the equation utx = uxyuy – uyyux
- Some harmonic Robin functions in the complex plane
- Ricci curvature and conformality of Riemannian manifolds to spheres
- A nonlinear integral equation for numerical conformal mapping
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- Dynamic random walks in Clifford algebras
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