Commutator Characterisation of Pseudo-differential Operators
On a smooth closed manifold the pseudo-differential operators can be characterised by taking commutators with vector fields, i.e., first-order partial derivatives. This approach is due to Beals (, 1977), Dunau (, 1977), and Coifman and Meyer (, 1978); perhaps the first ones to consider these kind of commutator properties were Calderón and his school . For other contributions, see also ,  and .
KeywordsSobolev Space Compact Manifold Closed Manifold Orientable Manifold Leibniz Formula
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