# Uncentered maximal function for elliptic partial differential operator

## TL;DR

This paper investigates the boundedness of the uncentered maximal function related to the Weinstein operator in harmonic analysis, establishing key estimates and weak-type inequalities on Lp spaces for p>1.

## Contribution

It introduces new boundedness results for the uncentered maximal function associated with the Weinstein operator, including estimates and weak-type inequalities.

## Key findings

- Boundedness of the uncentered maximal function on Lp for p>1
- Estimates for Weinstein translation of characteristic functions
- Weak-type L1-estimates for the maximal function

## Abstract

The present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius " centered at 0 on the upper half space. Second, we prove weak-type L1-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain that is bounded on Lp for p>1.