An $H^p$ scale for complete Pick spaces

Abstract

We define by interpolation a scale analogous to the Hardy $H^p$ scale for complete Pick spaces, and establish some of the basic properties of the resulting spaces, which we call $\mathcal{H}^p$. In particular, we obtain an $\mathcal{H}^p-\mathcal{H}^q$ duality and establish sharp pointwise estimates for functions in $\mathcal{H}^p$.