# The Hardy-Lorentz Spaces $H^{p,q}(R^n)$

## TL;DR

This paper explores the properties of Hardy-Lorentz spaces $H^{p,q}(R^n)$, focusing on atomic decomposition, interpolation, and operator behavior for $0<p extless 1$ and $0<q extless \infty$, advancing harmonic analysis understanding.

## Contribution

It provides new insights into atomic decomposition, interpolation, and operator boundedness in Hardy-Lorentz spaces, extending classical harmonic analysis results.

## Key findings

- Atomic decomposition of $H^{p,q}(R^n)$ established.
- Interpolation properties characterized.
- Boundedness of singular integrals on these spaces demonstrated.

## Abstract

In this paper we consider the Hardy-Lorentz spaces $H^{p,q}(R^n)$, with $0<p\le 1$, $0<q\le \infty$. We discuss the atomic decomposition of the elements in these spaces, their interpolation properties, and the behavior of singular integrals and other operators acting on them.