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We prove the existence of approximate solutions in the (regular)Denjoy-Carleman sense for some systems of smooth complex vector fields. Suchapproximate solutions provide a well defined notion of Denjoy-Carleman wavefront set of distributions on maximally real submanifolds in complex spacewhich can be characterized in terms of the decay of theFourier-Bros-Iagolnitzer transform. We also apply the approximate solutions toanalyze the Denjoy-Carleman microlocal regularity of solutions of certainsystems of first-order nonlinear partial differential equations.

Denjoy-Carleman Microlocal Regularity on Smooth Real Submanifolds of Complex Space