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arXiv · 1801.09000

Singular integrals and Hardy type spaces for the inverse Gauss measure

Tommaso Bruno
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Abstract

Let $\gamma_{-1}$ be the absolutely continuous measure on $\mathbb{R}^n$ whose density is the reciprocal of a Gaussian and consider the natural weighted Laplacian $\mathcal{A}$ on $L^2(\gamma_{-1})$. In this paper, we prove boundedness and unboundedness results for the purely imaginary powers and the first order Riesz transforms associated with the translated operators $\mathcal{A}+\lambda I$, $\lambda\geq0$, from certain new Hardy-type spaces adapted to $\gamma_{-1}$ to $L^1(\gamma_{-1})$. We also investigate the weak type $(1,1)$ of these operators.

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Tommaso Bruno. 2018-01-26. Singular integrals and Hardy type spaces for the inverse Gauss measure. https://arxiv.org/abs/1801.09000

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