# Lower bounds for estimates of the Schr\"odinger maximal function

## TL;DR

This paper establishes new lower bounds for the $L^p$ estimates of the Schrödinger maximal function by extending Bourgain's example, advancing understanding of the function's behavior in harmonic analysis.

## Contribution

The paper introduces generalized lower bounds for the Schrödinger maximal function estimates, building upon Bourgain's foundational example.

## Key findings

- New lower bounds for $L^p$ estimates established
- Generalization of Bourgain's example demonstrated
- Advances in understanding Schrödinger maximal function behavior

## Abstract

We give new lower bounds for $L^p$ estimates of the Schr\"odinger maximal function by generalizing an example of Bourgain.