Complex interpolation of $Z$-spaces

TL;DR

This paper establishes that Z-spaces form a complex interpolation scale across a broad parameter range, filling a gap in the mathematical theory of function spaces.

Contribution

It proves that Z-spaces $Z^{p,q}_s$ form a complex interpolation scale for all relevant parameters, extending previous partial results.

Findings

Z-spaces form a complex interpolation scale for all $0 < p,q ext{ and } s ext{ in } eal$

Fills a gap in the existing theory of Z-spaces

Complements recent work with Pascal Auscher

Abstract

We prove that the $Z$-spaces $Z^{p,q}_s$ form a complex interpolation scale for all $0 < p,q \leq \infty$ and $s \in \mathbb{R}$, filling a gap in recent work with Pascal Auscher.