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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2024, Number 1, Pages 69–76
DOI: https://doi.org/10.26907/0021-3446-2024-1-69-76 (Mi ivm9950) 		 
On maximal operators associated with singular hypersurfaces

S. E. Usmanov

Samarkand State University named after Sh. Rashidov, 15 Universitetski blvd., Samarkand, 140104 Republic of Uzbekistan
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DOI: https://doi.org/10.26907/0021-3446-2024-1-69-76
Abstract: Maximal operators associated with singular hypersurfaces in multidimensional Euclidean spaces are considered. We prove the boundedness of these operators and define a critical exponent in the space of summable functions, when hypersurfaces are given by parametric equations.
Keywords: maximal operator, averaging operator, fractional power series, critical exponent, singular hypersurface.
Received: 23.12.2022
Revised: 15.02.2023
Accepted: 29.03.2023
Document Type: Article
UDC: 517
Language: Russian
Citation: S. E. Usmanov, “On maximal operators associated with singular hypersurfaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 1, 69–76
Citation in format AMSBIB
\Bibitem{Usm24}
\by S.~E.~Usmanov
\paper On maximal operators associated with singular hypersurfaces
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2024
\issue 1
\pages 69--76
\mathnet{http://mi.mathnet.ru/ivm9950}
\crossref{https://doi.org/10.26907/0021-3446-2024-1-69-76}
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