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Matematicheskie Zametki, 2021, Volume 109, Issue 5, Pages 643–663
DOI: https://doi.org/10.4213/mzm12744 (Mi mzm12744) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Randol Maximal Functions and the Integrability of the Fourier Transform of Measures

D. I. Akramova, I. A. Ikromov

A. Navoi Samarkand State University
Full-text PDF (602 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm12744
Abstract: Estimates of the Fourier transform of charges (measures) concentrated on smooth hypersurfaces are considered. Following M. Sugumoto, three classes of smooth hypersurfaces are defined. Depending on the class, estimates of the Fourier transform of charges are obtained in terms of Randol maximal functions. The obtained estimates are applied to the solution of the integrability problem for the Fourier transform of measures concentrated on some nonconvex hypersurfaces. The sharpness of the obtained estimates is shown.
Keywords: measure, Fourier transform, hypersurface, curvature, integrability.
Funding agency Grant number
Commitee for coordination science and technologies under Cabinet Ministers of the Republic of Uzbekistan ОТ-Ф-4-69
This work was supported by the Executive Committee for the Coordination of Science and Technology under the Council of Ministers of the Republic of Uzbekistan (grant OT-F-4-69).
Received: 08.04.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 5, Pages 661–678
DOI: https://doi.org/10.1134/S0001434621050011
Bibliographic databases:
Document Type: Article
UDC: 517.518.5
Language: Russian
Citation: D. I. Akramova, I. A. Ikromov, “Randol Maximal Functions and the Integrability of the Fourier Transform of Measures”, Mat. Zametki, 109:5 (2021), 643–663; Math. Notes, 109:5 (2021), 661–678
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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