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On the Fefferman-Phong inequality. (Sur l’inégalité de Fefferman-Phong.) (French) Zbl 1086.35529
The author investigates the validity for a pseudo-differential operator \(A\) of the estimates \((Af,f)\geq-C\|f\|_{L^2}^2\). The operator \(A\) is assumed to be selfadjoint, that is, using the Weyl quantization \(A=a^w(x,D)\), the symbol \(a(x,\xi)\) is assumed to be nonnegative. Several results are presented, extending the Gårding and Fefferman-Phong inequalities in the frame of the Weyl-Hörmander calculus; in particular the author proves that if \(|D_x^\alpha D_\xi^\beta a(x,\xi)|\leq C\) for \(|\alpha+\beta|\geq4\), then the above estimates are satisfied.

35S05 Pseudodifferential operators as generalizations of partial differential operators
47G30 Pseudodifferential operators
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