# Boundedness of singular integrals on the flag Hardy spaces on Heisenberg group

## TL;DR

This paper proves the boundedness of classical singular integrals on multiparameter flag Hardy spaces on the Heisenberg group, revealing intermediate dilation properties between known dilation types.

## Contribution

It establishes the boundedness of convolution singular integrals on flag Hardy spaces on the Heisenberg group, a novel result in multiparameter harmonic analysis.

## Key findings

- Classical singular integrals are bounded on flag Hardy spaces.
- Intermediate dilation properties are identified between anisotropic and product dilations.
- The results extend understanding of harmonic analysis on the Heisenberg group.

## Abstract

We prove that the classical one-parameter convolution singular integrals on the Heisenberg group are bounded on multiparameter flag Hardy spaces, which satisfy `intermediate' dilation between the one-parameter anisotropic dilation and the product dilation on $\mathbb{C}^{n}\times \mathbb{R}$ implicitly.