Some intersections of Lorentz spaces

TL;DR

This paper introduces and characterizes new intersections of Lorentz spaces on measure spaces, expanding the understanding of their structure and relationships.

Contribution

It defines and analyzes specific intersections of Lorentz spaces, providing new insights into their properties and potential applications.

Findings

Characterization of ILp,Q(X,) spaces

Introduction of ILJ,q(X,) and ILJ,Q(X,) spaces

Structural properties of the new Lorentz space intersections

Abstract

Let (X,\mu) be a measure space. For p, q\in (0,\infty] and arbitrary subsets P,Q of (0,\infty], we introduce and characterize some intersections of Lorentz spaces, denoted by ILp,Q(X,\mu), ILJ,q(X,\mu) and ILJ,Q(X,\mu).