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

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 $0<p\le n$, 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.