Geodesic
On the Riesz transforms for the inverse Gauss measure
Tommaso Bruno1 ; Peter Sjögren2
1 Politecnico di Torino, Dipartimento di Scienze Matematiche "Giuseppe Luigi Lagrange" and Ghent University, Department of Mathematics: Analysis, Logic and Discrete Mathematics
2 Chalmers University of Technology, Mathematical Sciences and University of Gothenburg, Mathematical Sciences
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 433-448

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Let $\gamma_{-1}$ be the absolutely continuous measure on $\mathbf{R}^n$ whose density is the reciprocal of a Gaussian function. Let further $\mathscr{A}$ be the natural self-adjoint Laplacian on $L^2(\gamma_{-1})$. 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.
Keywords: Inverse Gauss measure, Riesz transforms, weak type (1, 1)

Tommaso Bruno 1 ; Peter Sjögren 2

1 Politecnico di Torino, Dipartimento di Scienze Matematiche "Giuseppe Luigi Lagrange" and Ghent University, Department of Mathematics: Analysis, Logic and Discrete Mathematics
2 Chalmers University of Technology, Mathematical Sciences and University of Gothenburg, Mathematical Sciences 
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Tommaso Bruno; Peter Sjögren. On the Riesz transforms for the inverse Gauss measure. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 433-448. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a24/