The boundedness of maximal operators associated with singular surfaces

DOI10.3103/S1066369X21060086zbMath1468.42021OpenAlexW3180025412MaRDI QIDQ2041630

S. E. Usmanov

Publication date: 23 July 2021

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x21060086

zbMATH Keywords

maximal operatorsingular surfaceaveraging operatorfractional power seriesnonsingular point

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Singularities of surfaces or higher-dimensional varieties (14J17)

Related Items (2)

On the boundedness of the maximal operators associated with singular hypersurfaces ⋮ On the boundedness problem of maximal operators

Cites Work

• Averages of functions over hypersurfaces in \(\mathbb R^n\)
• Averages in the plane over convex curves and maximal operators
• Estimates for maximal functions associated with hypersurfaces in \(\mathbb R^3\) and related problems of harmonic analysis
• An elementary coordinate-dependent local resolution of singularities and applications
• Maximal averages over surfaces
• Damped oscillatory integrals and boundedness of maximal operators associated to mixed homogeneous hypersurfaces
• Oscillatory integrals and maximal averages over homogeneous surfaces
• A multi-dimensional resolution of singularities with applications to analysis
• Inequalities for Some Maximal Functions. II
• Maximal functions: Spherical means
• Averages Over Convex Hypersurfaces
• On averaging operators associated with convex hypersurfaces of finite type
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