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.
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Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 133–143 https://doi.org/10.4213/mzm13967.
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Usmanov, S.E. On the Boundedness of the Maximal Operators Associated with Singular Hypersurfaces. Math Notes 114, 108–116 (2023). https://doi.org/10.1134/S0001434623070118
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DOI: https://doi.org/10.1134/S0001434623070118