On the structure of $\mathcal{N}_p$-spaces in the ball

TL;DR

This paper investigates the structure of $ _p$-spaces within the ball, demonstrating their Moebius-invariance and the distinctness of these spaces for certain p-values, with implications for operator theory.

Contribution

It establishes the Moebius-invariance of $ _p$-spaces and proves their distinctness for all $0<p extless= n$, advancing understanding of their structure.

Findings

$ _p$-spaces are Moebius-invariant

All $ _p$-spaces are different for $0<p extless= n$

Results have applications in operator theory

Abstract

We study the structure of $\mathcal{N}_p$-spaces in the ball. In particular, we show that any such space is Moebius-invariant and for $0<p \leq n$, all $\mathcal{N}_p$-spaces are different. Our results will be of important uses in the study of operator theory on $\mathcal{N}_p$-spaces.