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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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
Keywords
- Discrete harmonic analysis
- Jacobi polynomials
- Riesz transforms
- Weighted norm inequalities
- Discrete Calderón-Zygmund theory