A Note on Hardy Spaces on Quadratic CR Manifolds

Given a quadratic CR manifold $\mathcal{M}$ embedded in a complex space, and a holomorphic function $f$ on a tubular neighbourhood of $\mathcal{M}$, we show that the $L^p$-norms of the restriction of $f$ to the translates of $\mathcal{M}$ is decreasing for the ordering induced by the closed convex envelope of the image of the Levi form of $\mathcal{M}$.