# 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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