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arXiv · 2509.16148

On Tent Spaces for the Gaussian Measure

Liliana Forzani·Roberto Scotto·Wilfredo Urbina
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Abstract

Following the scheme of tent spaces in classical harmonic analysis developed by R. Coifman, Y. Meyer, and E. Stein in \cite{cms}, we succeed in doing so for the Gaussian setting. In \cite{MNP}, part of this theory (an atomic decomposition) is developed for a specific tent space where functions are defined just in a proper subset of $\mathbb{R}^{n+1}_+,$ and without the use of an area function. In the present paper, using a variation of the area function considered in \cite{FSU}, we define the Gaussian area function and Gaussian tent spaces and prove both their atomic decompositions and the characterization of their dual spaces. Some applications are also considered.

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Liliana Forzani, Roberto Scotto, Wilfredo Urbina. 2025-09-19. On Tent Spaces for the Gaussian Measure. https://arxiv.org/abs/2509.16148

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