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 ${\mathcal{H}}^p$.

References in corpus (2)

• Interpolating sequences in spaces with the complete Pick property
• Multipliers and operator space structure of weak product spaces