A characterization of the inclusions between mixed norm spaces

TL;DR

This paper provides a complete characterization of the inclusion relations between different Hardy-type mixed norm spaces, clarifying how parameters influence their structure and relationships.

Contribution

It offers a full description of when one Hardy-type mixed norm space is included in another based on their defining parameters.

Findings

Complete characterization of inclusion relations between $H(p,q,eta)$ and $H(u,v,eta)$ spaces.

Clarification of how parameters $p, q, eta, u, v$ affect space inclusion.

Extension of previous partial results to a comprehensive framework.

Abstract

We consider the mixed norm spaces of Hardy type studied by Flett and others. We study some properties of these spaces related to mean and pointwise growth and complement some partial results by various authors by giving a complete characterization of the inclusion between $H(p,q,\alpha)$ and $H(u,v,\beta),$ depending on the parameters $p, q, \alpha, u, v$ and $\beta.$