OSCILLATORY INTEGRALS RELATED TO CARLESON'S THEOREM

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L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates (2015, methodology): “Using the method of the proof of the multi-dimensional version of van der Corput lemma in [21] we may estimate | N (ξ) − cN (ξ)| = ∣ ∣∣ ∣ ∫”
ψ-pseudodifferential operators and estimates for maximal oscillatory integrals (2007, result): “To some extent, this can be viewed as a related investigation to that of Stein and Wainger [18].”
The (Weak-L2) Boundedness of the Quadratic Carleson Operator (2007, methodology): “Further, using the TT ∗ method and a variant of van der Corput’s lemma, Stein and Wainger [10] extended this result for polynomials of any degree, but again without the first degree term.”
Weighted norm inequalities for maximally modulated singular integral operators (2005, background): “Naturally Theorems 2.4 and 2.5 can be extended to polynomials of degree k provided an a priori L p estimate is known to hold for H � 1(k) . This would allow one to replace � n(k) � by � n(k) in the theorem of Stein and Wainger [ SWa ].”