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arXiv · 1701.04936

Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space

Hong-Quan Li·Peter Sjögren
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Abstract

Let $v \ne 0$ be a vector in $\R^n$. Consider the Laplacian on $\R^n$ with drift $Δ_{v} = Δ+ 2v\cdot \nabla$ and the measure $dμ(x) = e^{2 \langle v, x \rangle} dx$, with respect to which $Δ_{v}$ 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.

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Hong-Quan Li, Peter Sjögren. 2017-01-18. Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space. https://arxiv.org/abs/1701.04936

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