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On the Generalization of Hörmander's Inequality

ABSTRACT We are concerned with a lower bound with a gain of k/2 + 1 derivatives for the class OP N m, k (X, Σ) of pesudodifferential operators with characteristics of even multiplicity k ≥ 2. In the case of double characteristics operators (k = 2), we recapture a well-known inequality due to Hörmander.