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We study function spaces that are related to square-integrable, irreducible,unitary representations of several low-dimensional nilpotent Lie groups. Theseare new examples of coorbit theory and yield new families of function spaces on$\mathbb{R}^d $. The concrete realization of the representation suggests thatthese function spaces are useful for generalized time-frequency analysis orphase-space analysis.

New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis