Journal of the Ramanujan Mathematical Society

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Maximal Functions along Hypersurfaces


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1 Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211019, India
     

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In this paper, we study the Lp-boundedness of maximal operators along a class of hypersurfaces in ℝn+1 given by the graph of a function. We use a factorisation technique, which gives a simple proof of the maximal theorem. The idea is to factorise the maximal operator along hypersurface into a one-dimensional maximal operator of Hardy-Littlewood type, and a dilated maximal operator associated with a compact hypersurface in ℝn.
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  • Maximal Functions along Hypersurfaces

Abstract Views: 276  |  PDF Views: 1

Authors

Ramesh Manna
Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211019, India
P. K. Ratnakumar
Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211019, India

Abstract


In this paper, we study the Lp-boundedness of maximal operators along a class of hypersurfaces in ℝn+1 given by the graph of a function. We use a factorisation technique, which gives a simple proof of the maximal theorem. The idea is to factorise the maximal operator along hypersurface into a one-dimensional maximal operator of Hardy-Littlewood type, and a dilated maximal operator associated with a compact hypersurface in ℝn.

References