A new class of function spaces generalizing the Arias-de-Reyna space

TL;DR

This paper introduces a new class of rearrangement-invariant quasi-Banach spaces, $QA_{,}$, generalizing the classical $QA$ space, and explores their properties and relationships with other spaces.

Contribution

It defines and analyzes the structure of $QA_{,}$ spaces, extending the classical $QA$ space and studying their properties and connections.

Findings

$QA_{,}$ spaces generalize classical $QA$ spaces.

Basic properties of $QA_{,}$ are established.

Relationships with other rearrangement-invariant Banach spaces are explored.

Abstract

This paper studies the structure and properties of a rearrangement-invariant quasi-Banach space $QA_{\varphi,\psi}$ which generalizes the classical space $QA$ introduced by Arias-de-Reyna in connection with the study of the pointwise almost everywhere convergence of Fourier series. We present basic properties of $QA_{\varphi,\psi}$ and explore the relationship between $QA_{\varphi,\psi}$ and other rearrangement-invariant Banach spaces.