A note on discrete fractional integral operators on the Heisenberg group

TL;DR

This paper studies a discrete fractional integral operator on the Heisenberg group and establishes nearly optimal results using a straightforward combinatorial approach.

Contribution

It introduces a discrete analogue of a fractional integral operator on the Heisenberg group and provides nearly sharp bounds with a simple combinatorial proof.

Findings

Established nearly sharp bounds for the discrete fractional integral operator

Developed a simple combinatorial argument for the analysis

Extended understanding of fractional operators on non-commutative groups

Abstract

We consider the discrete analogue of a fractional integral operator on the Heisenberg group, for which we are able to prove nearly sharp results by means of a simple argument of a combinatorial nature.