English

An $H^p$ scale for complete Pick spaces

Functional Analysis 2022-04-25 v2 Complex Variables

Abstract

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

Keywords

Cite

@article{arxiv.2005.08909,
  title  = {An $H^p$ scale for complete Pick spaces},
  author = {Alexandru Aleman and Michael Hartz and John E. McCarthy and Stefan Richter},
  journal= {arXiv preprint arXiv:2005.08909},
  year   = {2022}
}
R2 v1 2026-06-23T15:38:09.429Z