  Low-dimensional ultracold gases are created in the laboratory by confining
three-dimensional (3D) gases inside highly anisotropic trapping potentials.
Such trap geometries not only provide access to simulating one-dimensional (1D)
and two-dimensional (2D) physics, but also can be used to study how the system
crosses over towards a 3D system in the limit of weak confinement. In this
work, we study the signature in radio-frequency (RF) spectroscopy for both the
1D-to-3D and the 2D-to-3D crossovers, in spin-polarized Fermi gases. We solve
the two-body scattering T-matrix in the presence of strong harmonic confinement
and use it to evaluate the two-body bound state and the RF spectroscopy
transfer rate in the high frequency limit, covering both the
quasi-low-dimensional and 3D limits. We find that in order to understand the
dimensional crossover for spin-polarized Fermi gases with p-wave interactions,
one needs to take into account an emergent s-wave interaction.
