An $H^p$ scale for complete Pick spaces

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