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Pseudodifferential operators associated to hyperplane bundles. (English) Zbl 0574.58027
Rend. Sem. Mat., Torino, Fasc. Spec., Linear partial and pseudo-differential operators, Conv. Torino/Italy 1982, 7-40 (1983).
[For the entire collection see Zbl 0533.00013.]
The authors introduce a new class of pseudodifferential operators which contains the parametrices of certain non-elliptic hypoelliptic operators and (1) is naturally associated to any hyperplane bundle contained in the tangent bundle of a manifold, (2) do not depend on the presence or absence of a pseudoconvexity or involutive condition, (3) do not lose \(L^ p\) properties by using Fourier integral transform, (4) admit complete asymptotic calculus. The rapid survey of a standard theory of pseudodifferential operators and full proofs of the theorems for the construction are given.
Reviewer: V.Z.Enol’skij

MSC:
58J40 Pseudodifferential and Fourier integral operators on manifolds
Citations:
Zbl 0533.00013