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Transference for Banach Space Representations of Nilpotent Lie Groups. Part 2. Pedersen Multipliers

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Abstract

We characterize twisted convolutions associated with the Pedersen transform for unitary irreducible representations of nilpotent Lie groups. For \(1\le p<\infty \), we also prove the \(L^p\)-boundedness for the Pedersen \(L^p\)-multipliers in the case of unitary irreducible representations that are square-integrable modulo the center of the group under consideration, thus, generalizing an earlier result on Weyl multipliers associated to the pseudo-differential Weyl calculus.

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Acknowledgements

We wish to thank the Referees for several useful remarks.

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Authors and Affiliations

  1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania

    Ingrid Beltiţă & Daniel Beltiţă

  2. Departamento de Matemáticas and I.U.M.A., Universidad de Zaragoza, 50009, Zaragoza, Spain

    José E. Galé

Authors
  1. Ingrid Beltiţă
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  2. Daniel Beltiţă
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  3. José E. Galé
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Correspondence to Daniel Beltiţă.

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This research was partly supported by Project MTM2016-77710-P, fondos FEDER, Spain. The third-named author has also been supported by Project E26-17R, D.G. Aragón, Spain.

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Beltiţă, I., Beltiţă, D. & Galé, J.E. Transference for Banach Space Representations of Nilpotent Lie Groups. Part 2. Pedersen Multipliers. J Geom Anal 31, 12568–12593 (2021). https://doi.org/10.1007/s12220-021-00728-8

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  • DOI: https://doi.org/10.1007/s12220-021-00728-8

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