ON THE FEFFERMAN–PHONG INEQUALITY AND RELATED PROBLEMS

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Dispersive estimates for principally normal pseudodifferential operators (2004, methodology): “We first state the L 2 solvability result proved in [22].”
Strichartz estimates and local smoothing estimates for asymptotically flat Schr (2007, methodology): “This construction uses the FBI transform, an approach that is reminiscent of the earlier works [24, 25, 26] for the wave equation.”
Global parametrices and dispersive estimates for variable coefficient wave equations (2007, unknown): “An important role is played by the conjugation of pdo’s with respect to the phase space transform, for which we use some results from [34], [36].”
On the water-wave equations with surface tension (2009, background): “Related results were previously proved by Bony [10] (see also [31]) in the much more general setting of sharp G̊arding or FeffermanPhong inequalities.”