Let γ−1 be the absolutely continuous measure on Rn whose density is the reciprocal of a Gaussian function. Let further A be the natural self-adjoint Laplacian on L2(γ−1). In this paper, we prove that the Riesz transforms associated with A of order one or two are of weak type (1, 1), but that those of higher order are not.
On the Riesz transforms for the inverse Gauss measure
Bruno, Tommaso;
2021-01-01
Abstract
Let γ−1 be the absolutely continuous measure on Rn whose density is the reciprocal of a Gaussian function. Let further A be the natural self-adjoint Laplacian on L2(γ−1). In this paper, we prove that the Riesz transforms associated with A of order one or two are of weak type (1, 1), but that those of higher order are not.
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