On the Riesz transforms for the inverse Gauss measure

Journal article, 2021

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