An atomic decomposition characterization of flag Hardy spaces $H^p_F({\rr}^{n}\times{\rr}^m)$ with applications

TL;DR

This paper provides an atomic decomposition characterization of flag Hardy spaces with partial cancellation atoms and establishes a boundedness criterion for operators on these spaces.

Contribution

It introduces a new atomic decomposition for flag Hardy spaces with partial cancellation conditions and applies it to operator boundedness criteria.

Findings

Atomic decomposition with partial cancellation atoms established

Boundedness criterion for operators on flag Hardy spaces proven

Enhanced understanding of structure of flag Hardy spaces

Abstract

In this paper, we give an atomic decomposition characterization of flag Hardy spaces $H^p_F({\rr}^n\times {\rr}^m)$ for $0<p\le 1$, which were introduced in \cite{hl1}. A remarkable feature of atoms of such flag Hardy spaces is that these atoms have only partial cancellation conditions. As an application, we prove a boundedness criterion for operators on flag Hardy spaces.