On Estimates for Maximal Operators

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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