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On the Fefferman-Phong inequality

Abdesslam Boulkhemair (2008)

Annales de l’institut Fourier

We show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by n 2 + 4 + ϵ improving thus the bound 2 n + 4 + ϵ obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type S 0 , 0 0 , we show that this number is bounded by n + 4 + ϵ ; more precisely, for a non negative symbol a , the Fefferman-Phong inequality holds if ∂ x α ∂ ξ β a ( x , ξ ) are bounded for, roughly, 4 ≤ | α | + | β | ≤ n + 4 + ϵ . To obtain such results and others, we first prove an abstract result which says that...

Opérateurs pseudo-différentiels définis en un point

Ryuichi Ishimura (2006)

Annales Polonici Mathematici

We introduce the notion of pseudo-differential operators defined at a point and we establish a canonical one-to-one correspondence between such an operator and its symbol. We also prove the invertibility theorem for special type operators.

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