On the Boundedness of the Maximal Operators Associated with Singular Hypersurfaces

The paper deals with maximal operators associated with a family of singular hypersurfaces in the space . 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 m...

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Bibliographic Details
Published in:Mathematical Notes 2023-08, Vol.114 (1-2), p.108-116
Main Author: Usmanov, S. E.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Hyperspaces
Mathematics
Mathematics and Statistics
Operators
Parametric equations
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Summary:The paper deals with maximal operators associated with a family of singular hypersurfaces in the space . 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.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434623070118