Geodesic
Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space
Canadian journal of mathematics, Tome 73 (2021) no. 5, pp. 1278-1304

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DOI

Let $v \ne 0$ be a vector in ${\mathbb {R}}^n$. Consider the Laplacian on ${\mathbb {R}}^n$ 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. 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.
DOI : 10.4153/S0008414X20000486
Mots-clés : Riesz transform, Littlewood–Paley–Stein operators, Heat semigroup, Laplacian with drift 
Li, Hong-Quan; Sjögren, Peter. Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space. Canadian journal of mathematics, Tome 73 (2021) no. 5, pp. 1278-1304. doi: 10.4153/S0008414X20000486
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     title = {Sharp endpoint estimates for some operators associated with the {Laplacian} with drift in {Euclidean} space},
     journal = {Canadian journal of mathematics},
     pages = {1278--1304},
     year = {2021},
     volume = {73},
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     doi = {10.4153/S0008414X20000486},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000486/}
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