We consider the maximal operators whose averages are taken over some non-smooth and non-convex hypersurfaces. For each 1 ≤ i ≤ d−1, let φi: [−1,1] → R be a continuous function satisfying some derivative conditions, and let (Formula presented). We prove the Lp boundedness of the maximal operators associated with the graph of φ which is a non-smooth and non-convex hypersurface in Rd, d ≥ 3.
- Maximal averages
- Non-smooth and non-convex hypersurfaces
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