Maximal Averages over Certain Non-smooth and Non-convex Hypersurfaces

Abstract

We consider the maximal operators whose averages are taken over some non-smooth and non-convex hypersurfaces. For each 1 <= i <= d - 1, let phi, : [-1, 1] -> be a continuous function satisfying some derivative conditions, and let phi(y) =Sigma(i=1)(d-1 )phi i(y(i) )We prove the L-P boundedness of the maximal operators associated with the graph of L-p which is a non-smooth and non-convex hypersurface in R-d , d >= 3.