Riesz transforms associated with the Grushin operator with drift

TL;DR

This paper investigates the boundedness properties of Riesz transforms linked to the Grushin operator with drift, which is symmetric under a measure with exponential growth, across various L^p spaces.

Contribution

It provides new results on the strong and weak type boundedness of Riesz transforms associated with the Grushin operator with drift.

Findings

Proves strong-type (p,p) boundedness for 1 < p < ∞

Establishes weak-type (1,1) boundedness

Analyzes the operator's behavior under exponential measure growth

Abstract

We consider the Grushin operator with drift which is symmetric with respect to a measure having exponential growth. For the corresponding Riesz transforms, we study strong-type $(p, p)$, $1 < p < \infty$, and weak-type $(1, 1)$ boundedness.