Abstract
The paper deals with boundedness problem for maximal operators associated to hypersurfaces in the space of integrable functions with degree p. A necessary condition for boundedness is given in the space of square-integrable functions in the case one nonvanishing principal curvature. A criterion for the boundedness of the maximal operators in the space of square-integrable functions is obtained for a partial class of convex hypersurfaces.
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Ikromov, I.A., Barakayev, A.M. On Estimates for Maximal Operators. Russ Math. 67, 17–26 (2023). https://doi.org/10.3103/S1066369X23070034
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DOI: https://doi.org/10.3103/S1066369X23070034