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

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.

19 pages