$\boldkey{L}^{\boldkey 2}$-estimates for a class of singular oscillatory integrals

We prove $L^2$ estimates for singular integral operators with oscillatory terms and consequently obtain new results for Hilbert transforms along variable curves in the plane. In particular we extend a result of Nagel, Vance, Wainger and Weinberg for translation invariant even curves.

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Published 1 January 1994