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Semi-elliptic operators generated by vector fields

E. Shargorodsky — 2002

Let M be a C -smooth n-dimensional manifold and ν₁, ..., νₙ be C -smooth vector fields on M which span the tangent space T x M at each point x ∈ M. The vector fields ν₁, ..., νₙ may have nonzero commutators. We construct a calculus of pseudodifferential operators (ψDOs) which act on sections of vector bundles over M and have symbols belonging to anisotropic analogues of the Hörmander classes S ϱ , δ r , and apply it to semi-elliptic operators generated by ν₁,...,νₙ. The results obtained include the formula expressing...

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