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Funktsional'nyi Analiz i ego Prilozheniya, 2015, Volume 49, Issue 3, Pages 74–79
DOI: https://doi.org/10.4213/faa3190 (Mi faa3190) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

Integrability of the Fourier Transforms of Measures Concentrated on Hypersurfaces

I. A. Ikromov

A. Navoi Samarkand State University
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DOI: https://doi.org/10.4213/faa3190
Abstract: This paper considers estimates for the Fourier transforms of signed measures concentrated on families of hypersurfaces. A theorem about the integrability of Randol-type maximal functions related to a certain class of nonconvex hypersurfaces is presented. The results are applied to study the integrability of the Fourier transforms of signed measures concentrated on certain hypersurfaces. In a special case, the exact integrability exponent of the Fourier transforms of measures is specified. The results improve a recent theorem of L. Erdős and M. Salmhofer.
Keywords: asymptotics, Fourier transforms, integrability, curvature.
Funding agency Grant number
Исполнительный комитет по координации науки и технологий при КМ Республики Узбекистан Ф-4-17
Received: 18.08.2013
English version:
Functional Analysis and Its Applications, 2015, Volume 49, Issue 3, Pages 218–221
DOI: https://doi.org/10.1007/s10688-015-0108-x
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: I. A. Ikromov, “Integrability of the Fourier Transforms of Measures Concentrated on Hypersurfaces”, Funktsional. Anal. i Prilozhen., 49:3 (2015), 74–79; Funct. Anal. Appl., 49:3 (2015), 218–221
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa/v49/i3/p74
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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