# Variable exponent Hardy spaces associated with discrete Laplacians on graphs

## TL;DR

This paper develops the theory of variable exponent Hardy spaces on infinite graphs with discrete Laplacians, including their atomic decompositions and boundedness of key operators, advancing harmonic analysis on graph structures.

## Contribution

It introduces a new framework for variable exponent Hardy spaces on graphs and analyzes the boundedness of classical harmonic analysis operators within this setting.

## Key findings

- Established atomic and molecular decompositions for these Hardy spaces.
- Proved boundedness of Littlewood-Paley functions, Riesz transforms, and spectral multipliers.
- Extended harmonic analysis tools to variable exponent spaces on graphs.

## Abstract

In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.