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Journal of the Ramanujan Mathematical Society

Volume 33, Issue 3, September 2018  pp. 283–296.

Maximal functions along hypersurfaces

Authors:  Ramesh Manna and P. K. Ratnakumar
Author institution:Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211 019, India

Summary:  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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