L^p -Bounds for Pseudo-differential Operators on Graded Lie Groups

In this work we obtain sharp L^p-estimates for pseudo-differential operators on arbitrary graded Lie groups. The results are presented within the setting of the global symbolic calculus on graded Lie groups by using the Fourier analysis associated to every graded Lie group which extends the usual one due to Hörmander on Rⁿ. The main result extends the classical Fefferman’s sharp theorem on the L^p-boundedness of pseudo-differential operators for Hörmander classes on Rⁿ to general graded Lie groups, also adding the borderline ρ= δ case.