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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