On the Riesz transforms for the inverse Gauss measure

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