# Martingale Hardy-Amalgam Spaces: Atomic decompositions and duality

## TL;DR

This paper introduces martingale Hardy-amalgam spaces, provides atomic decompositions for them, and characterizes their dual spaces as Campanato-type spaces, advancing the theoretical framework of martingale function spaces.

## Contribution

It defines new martingale Hardy-amalgam spaces, establishes atomic decompositions, and identifies their dual spaces, extending the understanding of martingale function space duality.

## Key findings

- Atomic decompositions for $H^s_{p,q}$, $\,\, ext{and}\,\, ext{other spaces}$
- Dual space of $H^s_{p,q}$ is a Campanato-type space for $0<p extless q extless 1$
- New framework for martingale Hardy-amalgam spaces

## Abstract

In this paper, we introduce the notion of martingale Hardy-amalgam spaces: $ H^s_{p,q},\,\,\mathcal{Q}_{p,q}$ and $\mathcal{P}_{p,q}$. We present two atomic decompositions for these spaces. The dual space of $H^s_{p,q}$ for $0<p\le q\le 1$ is shown to be a Campanato-type space.