An $H^p$ scale for complete Pick spaces
Volume 258 / 2021
Studia Mathematica 258 (2021), 343-359
MSC: Primary 46E22; Secondary 46B70, 47B35.
DOI: 10.4064/sm200514-18-9
Published online: 9 December 2020
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 $\mathcal {H}^p$.
