# 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.

1)$weak type$(1

Riesz transforms

Inverse Gauss measure

## Author

### Tommaso Bruno

University Hospital of Ghent

### Peter Sjögren

Chalmers, Mathematical Sciences

1239-629X (ISSN)

Vol. 46 1-16

### Subject Categories

Mathematical Analysis

### DOI

10.5186/aasfm.2021.4609