Summability of oscillatory integrals over parameters and the boundedness problem for fourier transforms on curves

We find the exact exponent of summability of the Fourier transform of signed measures concentrated on differentiable curves of finite type. We study the behavior of oscillatory integral operators related to the Fourier transform of signed measures concentrated on curves. We obtain necessary and sufficient conditions for the boundedness of the Fourier transform on smooth curves of finite type.

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