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Let M be a -smooth n-dimensional manifold and ν₁, ..., νₙ be -smooth vector fields on M which span the tangent space 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 , and apply it to semi-elliptic operators generated by ν₁,...,νₙ. The results obtained include the formula expressing...
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