On Estimates for Maximal Operators
Isroil A. IkromovRomanovsky Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, 140104, Samarkand, Republic of UzbekistanAkmal BarakayevSamarkand State University, 140104, Samarkand, Republic of Uzbekistan
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Аннотация
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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