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arXiv · 1906.03827

On the Riesz Transforms for the inverse Gauss measure

Tommaso Bruno·Peter Sjögren
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Abstract

Let $γ_{-1}$ be the absolutely continuous measure on $\mathbb{R}^n$ whose density is the reciprocal of a Gaussian function. Let further $\mathscr{A}$ be the natural self-adjoint Laplacian on $L^2(γ_{-1})$. In this paper, we prove that the Riesz transforms associated with $\mathscr{A}$ of order one or two are of weak type $(1,1)$, but that those of higher order are not.

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Tommaso Bruno, Peter Sjögren. 2021-03-12. On the Riesz Transforms for the inverse Gauss measure. https://arxiv.org/abs/1906.03827

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