L^p boundedness of maximal averages over hypersurfaces in R^3

TL;DR

This paper proves an L^p boundedness theorem for maximal averages over hypersurfaces in three-dimensional space, extending previous methods and providing sharp estimates for p > 2, contributing to the ongoing research in harmonic analysis.

Contribution

It introduces a new approach using adapted coordinate systems to establish sharp L^p bounds for maximal operators over hypersurfaces in R^3.

Findings

Proves L^p boundedness for p > 2

Provides sharp estimates when p is optimal

Offers an alternative method to recent related work

Abstract

Extending the methods developed in the author's previous paper and using adapted coordinate systems in two variables, an L^p boundedness theorem is proven for maximal operators over hypersurfaces in R^3 when p > 2. When the best possible p is greater than 2, the theorem typically provides sharp estimates. This gives another approach to the subject of recent work of Ikromov, Kempe, and Muller on this subject