# Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space. Journal article, 2020

Let $v \ne 0$ be a vector in $\R^n$. Consider the Laplacian on $\R^n$ with drift $\Delta_{v} = \Delta + 2v\cdot \nabla$ and the measure $d\mu(x) = e^{2 \langle v, x \rangle} dx$, with respect to which $\Delta_{v}$ is self-adjoint. %Let $d$ and $\nabla$ denote the Euclidean distance and the gradient operator on $\R^n$. Consider the space $(\R^n, d,d\mu)$, which has the property of exponential volume growth. This measure has exponential growth with respect to the Euclidean distance. We study weak type $(1, 1)$ and other sharp endpoint estimates for the Riesz transforms of any order, and also for the vertical and horizontal Littlewood-Paley-Stein functions associated with the heat and the Poisson semigroups.

Littlewood-Paley-Stein operators

Laplacian with drift

Heat semigroup

Riesz transform

## Author

Fudan University

### Peter Sjögren

Chalmers, Mathematical Sciences

University of Gothenburg

#### Canadian Journal of Mathematics

0008-414X (ISSN) 1496-4279 (eISSN)

Vol. In Press

Mathematics

Basic sciences

### DOI

10.4153/S0008414X20000486

12/16/2020