# Multilinear Fractional Integral Operators: A counter-example

## TL;DR

This paper presents a counter-example demonstrating that multilinear fractional operators are not bounded from a product of Hardy spaces into a Hardy space, challenging previous assumptions about their boundedness properties.

## Contribution

The paper provides the first explicit counter-example showing the unboundedness of multilinear fractional operators on Hardy spaces.

## Key findings

- Multilinear fractional operators are not bounded from a product of Hardy spaces into a Hardy space.
- Counter-example disproves previous conjectures about boundedness.
- Highlights limitations of multilinear fractional operators in harmonic analysis.

## Abstract

By means of a counter-example we show that the multilinear fractional operator is not bounded from a product of Hardy spaces into a Hardy space.