Sobolev spaces, Lebesgue points and maximal functions

TL;DR

This paper investigates the boundedness of various maximal operators within Sobolev spaces, including the spherical maximal operator, and examines the measure of Lebesgue points related to these operators.

Contribution

It introduces new results on the boundedness of a broad class of maximal operators in Sobolev spaces and analyzes Lebesgue point sets for these operators.

Findings

Boundedness results for maximal operators in Sobolev spaces.

Analysis of Lebesgue point sets related to these maximal operators.

Extension of classical results to a wider class of operators.

Abstract

In this note we study boundedness of a large class of maximal operators in Sobolev spaces that includes the spherical maximal operator. We also study the size of the set of Lebesgue points with respect to convergence associated with such maximal operators.