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 \(\mathcal {J}^{(\alpha ,\beta )}\) 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 \(\mathcal {J}^{(\alpha ,\beta )}\). We make use of an appropriate discrete vector-valued local Calderón-Zygmund theory.

中文翻译：

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与Jacobi展开相关的离散谐波分析II：Riesz变换

目前的工作是我们的研究中的延续（竞技场等，J。数学。元素分析申请490（123996），21，2020）在有关雅可比膨胀离散谐波分析。拉普拉斯算子的作用是由归一化Jacobi多项式的三项递归关系所定义的算子\（\ mathcal {J} ^ {（\ alpha，\ beta}} \）所扮演。主要兴趣是为与\（\ mathcal {J} ^ {（\ alpha，\ beta}} \）相关联的Riesz变换建立加权不等式。我们利用适当的离散矢量值局部Calderón-Zygmund理论。