Dyadic Martingale Hardy-amalgam spaces: Embeddings and Duality

TL;DR

This paper investigates the relationships and duality properties of dyadic martingale Hardy-amalgam spaces, introducing new spaces and characterizations to deepen understanding of their structure.

Contribution

It provides new embeddings, duality characterizations, and introduces a Garsia-type space within dyadic martingale Hardy-amalgam spaces.

Findings

Embeddings of various dyadic martingale Hardy-amalgam spaces are established.

Dual spaces of $H^s_{p,q}$ and $ ext{G}_{p,q}$ are characterized.

New Garsia-type space $ ext{G}_{p,q}$ is introduced and analyzed.

Abstract

We present in this paper some embeddings of various dyadic martingale Hardy-amalgam spaces $H^S_{p,q},\,\, H^s_{p,q},\,\,H^*_{p,q},\,\,\mathcal{Q}_{p,q}$ and $\mathcal{P}_{p,q}$ of the real line. In the same settings, we characterize the dual of $H^s_{p,q}$ for large $p$ and $q$. We also introduce a Garsia-type space $\mathcal{G}_{p,q}$ and characterize its dual space.