Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space.
Journal article, 2021

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.

Riesz transform

Heat semigroup

Littlewood-Paley-Stein operators

Laplacian with drift


Hong-Quan Li

Fudan University

Peter Sjögren

University of Gothenburg

Chalmers, Mathematical Sciences

Canadian Journal of Mathematics

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

Vol. 73 5 1278-1304

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Basic sciences



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