ψ-pseudodifferential operators and estimates for maximal oscillatory integrals

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Global and local regularity of Fourier integral operators on weighted and unweighted spaces (2011, background): “As a consequence, we obtain an alternative proof for the L2 boundedness of pseudo-pseudodifferential operators introduced in [23].”
On the Hörmander Classes of Bilinear Pseudodifferential Operators (2009, methodology): “For completeness, we have provided another proof of the case p1 = p2 = ∞ of Theorem 2 following the arguments of the corresponding linear result in [20].”