Nicolas Lerner (2000)
Annales de l'institut Fourier
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This paper begins with a broad survey of the state of the art in matters of solvability for differential and pseudo-differential equations. Then we proceed with a Hilbertian lemma which we use to prove a new solvability result.
Pierre Degond (1986)
Annales scientifiques de l'École Normale Supérieure
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Hart F. Smith, Christopher D. Sogge (2000)
Annales scientifiques de l'École Normale Supérieure
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Linda Preiss Rothschild, David S. Tartakoff (1982)
Annales scientifiques de l'École Normale Supérieure
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Frédéric Hérau (2000)
Annales de l'institut Fourier
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In this article we give a complete proof in one dimension of an a priori inequality involving pseudo-differential operators: if and are symbols in such that , then for all we have the estimate for all in the Schwartz space, where is the usual norm. We use microlocalization of levels I, II and III in the spirit of Fefferman’s SAK principle.