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.
Advances in Pure and Applied Mathematics – de Gruyter
Published: Mar 1, 2010