Geodesic
On the Boundedness of the Maximal Operators Associated with Singular Hypersurfaces
Matematičeskie zametki, Tome 114 (2023) no. 1, pp. 133-143

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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
Mots-clés : singular hypersurface. 
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     author = {S. E. Usmanov},
     title = {On the {Boundedness} of the {Maximal} {Operators} {Associated} with {Singular} {Hypersurfaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {133--143},
     publisher = {mathdoc},
     volume = {114},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_1_a10/}
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S. E. Usmanov. On the Boundedness of the Maximal Operators Associated with Singular Hypersurfaces. Matematičeskie zametki, Tome 114 (2023) no. 1, pp. 133-143. http://geodesic.mathdoc.fr/item/MZM_2023_114_1_a10/