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

We characterize twisted convolutions associated with the Pedersen transform for unitary irreducible representations of nilpotent Lie groups. For 1 ≤ p < ∞ , we also prove the L p -boundedness for the Pedersen L p -multipliers in the case of unitary irreducible representations that are square-inte...

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Bibliographic Details
Published in:The Journal of geometric analysis 2021-12, Vol.31 (12), p.12568-12593
Main Authors: Beltiţă, Ingrid, Beltiţă, Daniel, Galé, José E.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Banach spaces
Convex and Discrete Geometry
Differential calculus
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Lie groups
Mathematics
Mathematics and Statistics
Multipliers
Representations
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Summary:We characterize twisted convolutions associated with the Pedersen transform for unitary irreducible representations of nilpotent Lie groups. For 1 ≤ p < ∞ , 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.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-021-00728-8