# Embeddings between grand, small and variable Lebesgue spaces

## TL;DR

This paper establishes conditions for embeddings between grand, small, and variable Lebesgue spaces, extending recent results and demonstrating near-optimality through constructed examples.

## Contribution

It provides new criteria for embeddings between these spaces and extends previous work by Rakotoson and Sbordone.

## Key findings

- Derived conditions for embeddings between Lebesgue spaces
- Constructed examples showing near-optimality of results
- Extended recent theoretical results in the field

## Abstract

We give conditions on the exponent function $p(\cdot)$ that imply the existence of embeddings between grand, small and variable Lebesgue spaces. We construct examples to show that our results are close to optimal. Our work extends recent results by the second author, Rakotoson and Sbordone.