Abstract
In the framework of the Weyl–Hörmander calculus, under a condition of “geodesic temperance”, pseudodifferential operators can be characterized by the boundedness of their iterated commutators. As a corollary, functions of pseudodifferential operators are themselves pseudodifferential. Sufficient conditions are given for the geodesic temperance. In particular, it is valid in the Beals–Fefferman calculus.
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2010 Mathematics Subject Classification:35S05, 47A60, 47G30.
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Bony, JM. (2013). On the Characterization of Pseudodifferential Operators (Old and New). In: Cicognani, M., Colombini, F., Del Santo, D. (eds) Studies in Phase Space Analysis with Applications to PDEs. Progress in Nonlinear Differential Equations and Their Applications, vol 84. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-6348-1_2
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DOI: https://doi.org/10.1007/978-1-4614-6348-1_2
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