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Matematicheskie Zametki, 2010, Volume 87, Issue 5, Pages 734–755
DOI: https://doi.org/10.4213/mzm4619 (Mi mzm4619) 		 
This article is cited in 9 scientific papers (total 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
Full-text PDF (639 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm4619
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
English version:
Mathematical Notes, 2010, Volume 87, Issue 5, Pages 700–719
DOI: https://doi.org/10.1134/S0001434610050093
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. A. Ikromov, “Summability of Oscillatory Integrals over Parameters and the Boundedness Problem for Fourier Transforms on Curves”, Mat. Zametki, 87:5 (2010), 734–755; Math. Notes, 87:5 (2010), 700–719
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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