On Tent Spaces for the Gaussian Measure

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.