This article is cited in 9 papers

Summability of Oscillatory Integrals over Parameters and the Boundedness Problem for Fourier Transforms on Curves

I. A. Ikromov

A. Navoi Samarkand State University

Abstract: 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.

Keywords: oscillatory integral, Fourier transform, exponent of summability, versal deformation, Randol function, differentiable curve, diffeomorphism group.

Received: 29.12.2008

DOI: 10.4213/mzm4619

 English version: Mathematical Notes, 2010, 87:5, 700–719

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