# Discrete Harmonic Analysis associated with Jacobi expansions II: the Riesz transform

## TL;DR

This paper extends discrete harmonic analysis for Jacobi expansions by studying weighted inequalities for the Riesz transform linked to the operator derived from Jacobi polynomial recurrences.

## Contribution

It introduces new weighted inequality results for the Riesz transform associated with the Jacobi-related operator, advancing the understanding of discrete harmonic analysis in this context.

## Key findings

- Established weighted inequalities for the Riesz transform
- Extended previous work on Jacobi expansions
- Provided new bounds for discrete harmonic analysis operators

## Abstract

This paper is the continuation of the study on discrete harmonic analysis related to Jacobi expansions initiated in [1]. Considering the operator $\mathcal{J}^{(\alpha,\beta)}=J^{(\alpha,\beta)}-I$, where $J^{(\alpha,\beta)}$ is the three-term recurrence relation for the normalized Jacobi polynomials and $I$ is the identity operator, we focus on the study of weighted inequalities for the Riesz transform associated with it.