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Mat. Zametki, 2010, Volume 87, Issue 5, Pages 734–755 (Mi mz4619)  

This article is cited in 3 scientific papers (total in 3 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

DOI: https://doi.org/10.4213/mzm4619

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

Bibliographic databases:

Received: 29.12.2008

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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  • https://doi.org/10.4213/mzm4619
  • http://mi.mathnet.ru/eng/mz/v87/i5/p734

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. A. Ikromov, “Integrability of the Fourier Transforms of Measures Concentrated on Hypersurfaces”, Funct. Anal. Appl., 49:3 (2015), 218–221  mathnet  crossref  crossref  isi  elib
    2. I. A. Ikromov, S. E. Usmanov, “Ob ogranichennosti maksimalnykh operatorov, svyazannykh s giperpoverkhnostyami”, Sovremennye problemy matematiki i fiziki, SMFN, 64, no. 4, Rossiiskii universitet druzhby narodov, M., 2018, 650–681  mathnet  crossref
    3. Safarov A.R., “On the l-P-Bound For Trigonometric Integrals”, Anal. Math., 45:1 (2019), 153–176  crossref  mathscinet  zmath  isi  scopus
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