Whitney coverings and the tent spaces $T^{1,q}(\gamma)$ for the Gaussian measure

TL;DR

This paper develops a new technique for Whitney decompositions in Gaussian harmonic analysis and applies it to study Gaussian analogues of classical tent spaces, advancing the understanding of function spaces under Gaussian measures.

Contribution

Introduces a novel method for Whitney decompositions in Gaussian harmonic analysis and extends classical tent space theory to Gaussian measures.

Findings

Established Gaussian tent space analogues of classical spaces

Developed a new Whitney decomposition technique for Gaussian analysis

Enhanced tools for Gaussian harmonic analysis

Abstract

We introduce a technique for handling Whitney decompositions in Gaussian harmonic analysis and apply it to the study of Gaussian analogues of the classical tent spaces $T^{1,q}$ of Coifman, Meyer and Stein.