Hardy spaces and dilations on homogeneous groups

TL;DR

This paper characterizes specific dilation groups on homogeneous groups that preserve Hardy spaces as defined by Folland and Stein, providing insights into the structure of these function spaces.

Contribution

It identifies and characterizes the dilation groups on homogeneous groups that keep Hardy spaces invariant, advancing understanding of their geometric and analytical properties.

Findings

Identified dilation groups preserving Hardy spaces

Provided criteria for Hardy space invariance under dilations

Enhanced understanding of Hardy spaces on homogeneous groups

Abstract

On a homogeneous group, we characterize the one-parameter groups of dilations whose associated Hardy spaces in the sense of Folland and Stein are the same.