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This paper is the continuation of the study on discrete harmonic analysisrelated 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 inequalitiesfor the Riesz transform associated with it.

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