### Cutting the loss of derivatives for solvability under condition $\left(\Psi \right)$

Nicolas Lerner (2006)

Bulletin de la Société Mathématique de France

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For a principal type pseudodifferential operator, we prove that condition $\left(\psi \right)$ implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from $\u03f5+3/2$ for any $\u03f5\>0$ (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition $\left(\psi \right)$ doesimply local solvability with a loss of 1...