Discrete Harmonic Analysis Associated with Jacobi Expansions II: the Riesz Transform

Abstract

The present work is the continuation of our study (Arenas et al. J. Math. Anal. Appl. 490(123996), 21, 2020) on discrete harmonic analysis related to Jacobi expansions. The role of a Laplacian is played by the operator J(α,β) defined by the three-term recurrence relation for the normalised Jacobi polynomials. The main interest is to establish weighted inequalities for the Riesz transform associated with J(α,β). We make use of an appropriate discrete vector-valued local Calderon-Zygmund theory.