# Interpolation theorem for Marcinkiewicz spaces with applications to Lorentz gamma spaces

## TL;DR

This paper establishes an interpolation theorem for Marcinkiewicz spaces using Hardy-type operators, providing new insights into their structure and applications to Lorentz gamma spaces with clear, elementary proofs.

## Contribution

It characterizes interpolation spaces between Marcinkiewicz spaces via Hardy type operators and explores their properties on Lorentz gamma spaces, offering new theoretical tools.

## Key findings

- Characterization of interpolation spaces between Marcinkiewicz spaces.
- Analysis of Hardy type operators on Lorentz gamma spaces.
- Elementary proofs of key properties and results.

## Abstract

This paper is devoted to the interpolation principle between spaces of weak type. We characterise interpolation spaces between two Marcinkiewicz spaces in terms of Hardy type operators involving suprema. We study general properties of such operators and their behavior on Lorentz gamma spaces. A particular emphasis is placed on elementary and comprehensive proofs.