Lower bounds for pseudo-differential operators

This paper contains some new results on lower bounds for pseudo-differential operators whose symbols do not remain positive. Non-negativity of averages of the symbol on canonical images of the unit ball is sufficient to get a Gårding type inequality for Schrödinger operators with magnetic potential and one dimensional pseudo-differential operators.

On some localized estimates for pseudo-differential operators

Anders Melin (1978)

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Classes of spatially inhomogeneous pseudodifferential operators

R. Beals, C. Fefferman (1972-1973)

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Pseudo-differential operators with symbols admitting negative values