Abstract:
The paper deals with maximal operators associated with a family of singular hypersurfaces in the space $\mathbb{R}^{n+1}$. 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.
Keywords:maximal operator, averaging operator, fractional power series, regular point, singular hypersurface.
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