# L^p estimates for Baouendi-Gru

## TL;DR

This paper establishes L^p estimates for the Baouendi-Grushin operator, extending known results to a broader class of weights and providing new insights into its analytical properties.

## Contribution

It introduces novel L^p estimates for the Baouendi-Grushin operator, including more general weights in the case p=2, advancing the understanding of its functional analysis.

## Key findings

- L^p estimates proved for the Baouendi-Grushin operator
- Extension to more general weights for p=2
- Enhanced understanding of operator's analytical properties

## Abstract

We prove L^p estimates for the Baouendi-Grushin operator L=Delta_x+|x|^\alpha Delta_y in L^p(R^N+M), 1 < p < 1, where x belongs to R^N; y belongs to R^M. When p = 2 more general weights belonging to Reverse Holder classes are allowed.