$L^p$-boundedness of Bergman projections for $\alpha$-parabolic operators

Abstract

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 [3] also for $n = 1$.