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Matematicheskie Zametki, 2023, Volume 114, Issue 1, Pages 133–143
DOI: https://doi.org/10.4213/mzm13967 (Mi mzm13967) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Boundedness of the Maximal Operators Associated with Singular Hypersurfaces

S. E. Usmanov

A. Navoi Samarkand State University
Full-text PDF (554 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm13967
Abstract: The paper deals with maximal operators associated with a family of singular hypersurfaces in the space $\mathbb{R}^{n+1}$. The boundedness of these operators in the space of integrable functions is proved for the case in which the singular hypersurfaces are given by parametric equations. The boundedness exponent of maximal operators for spaces of integrable functions is found.
Keywords: maximal operator, averaging operator, fractional power series, regular point, singular hypersurface.
Received: 14.01.2022
Revised: 13.01.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 1, Pages 108–116
DOI: https://doi.org/10.1134/S0001434623070118
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: S. E. Usmanov, “On the Boundedness of the Maximal Operators Associated with Singular Hypersurfaces”, Mat. Zametki, 114:1 (2023), 133–143; Math. Notes, 114:1 (2023), 108–116
Citation in format AMSBIB
\Bibitem{Usm23}
\by S.~E.~Usmanov
\paper On the Boundedness of the Maximal Operators Associated with Singular Hypersurfaces
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 1
\pages 133--143
\mathnet{http://mi.mathnet.ru/mzm13967}
\crossref{https://doi.org/10.4213/mzm13967}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4634777}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 1
\pages 108--116
\crossref{https://doi.org/10.1134/S0001434623070118}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85168580399}
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  • https://www.mathnet.ru/eng/mzm/v114/i1/p133
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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