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

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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 \(\mathcal {J}^{(\alpha ,\beta )}\) 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.

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Authors and Affiliations

  1. Departamento de Matemáticas y Computación, Universidad de La Rioja, Complejo Científico-Tecnológico, Calle Madre de Dios 53, Logroño, 26006, Spain

    Alberto Arenas, Óscar Ciaurri & Edgar Labarga

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  1. Alberto Arenas
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  2. Óscar Ciaurri
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  3. Edgar Labarga
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Correspondence to Óscar Ciaurri.

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The first-named author was partially supported by a predoctoral research grant of the Government of Comunidad Autónoma de La Rioja. The second-named author was supported by grant MTM2015-65888-C04-4-P MINECO/FEDER, UE, from Spanish Government. The third-named author was partially supported by a predoctoral research grant of the University of La Rioja.

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Arenas, A., Ciaurri, Ó. & Labarga, E. Discrete Harmonic Analysis Associated with Jacobi Expansions II: the Riesz Transform. Potential Anal 57, 501–520 (2022). https://doi.org/10.1007/s11118-021-09925-0

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  • DOI: https://doi.org/10.1007/s11118-021-09925-0

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