We consider the $\alpha$-parabolic Bergman spaces on strip domains. The Bergman kernel is given by a series of derivatives of the fundamental solution. We prove the $L^p$-boundedness of the projection defined by the Bergman kernel and obtain the duality theorem for $1 \lt p \lt \infty$. At the same time, we give a new proof of the Huygens property, which enable us to verify all the results in  also for $n = 1$.
Digital Object Identifier: 10.2969/aspm/04410305