# Multilinear fractional type operators and their commutators on Hardy spaces with variable exponents

## TL;DR

This paper investigates the boundedness and continuity of multilinear fractional type operators and their commutators on Hardy spaces with variable exponents, expanding understanding of their behavior in variable exponent function spaces.

## Contribution

It establishes boundedness of multilinear fractional operators from Hardy to Lebesgue spaces with variable exponents and analyzes the continuity of their commutators on these spaces.

## Key findings

- Boundedness of multilinear fractional operators on variable exponent Hardy and Lebesgue spaces.
- Continuity properties of commutators of these operators on Hardy spaces with variable exponents.
- Application of atomic decomposition theory to prove boundedness results.

## Abstract

In this article, we show that multilinear fractional type operators are bounded from product Hardy spaces with variable exponents into Lebesgue spaces with variable exponents via the atomic decomposition theory. We also study continuity properties of commutators of multilinear fractional type operators on product of certain Hardy spaces with variable exponents.