An $H^p$ scale for complete Pick spaces
Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter

TL;DR
This paper introduces a new scale of function spaces called $\\mathcal{H}^p$ for complete Pick spaces, extending Hardy $H^p$ concepts and establishing duality and pointwise estimates.
Contribution
It defines the $\\mathcal{H}^p$ scale for complete Pick spaces via interpolation and explores its fundamental properties, including duality and estimates.
Findings
Established $\\mathcal{H}^p-\\mathcal{H}^q$ duality
Derived sharp pointwise estimates for functions in $\\mathcal{H}^p$
Introduced a new interpolation-based scale for complete Pick spaces
Abstract
We define by interpolation a scale analogous to the Hardy scale for complete Pick spaces, and establish some of the basic properties of the resulting spaces, which we call . In particular, we obtain an duality and establish sharp pointwise estimates for functions in .
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