Zachary spaces ${\mathcal{Z}}^p[{\mathbb{R}}^{\infty }]$ and separable Banach spaces

Abstract

We construct Zachary space in ${\mathbb{R}}^{\infty }$ and find that this is a Banach space of functions of bounded mean oscillation with order $p,1\le p\le \infty$ containing the function of bounded mean oscillation $BMO[{\mathbb{R}}_I^{\infty }]$ as a dense continuous embedding. As an application of ${\mathbb{R}}_I^{\infty }$ we construction $\mcB,$ where $\mcB $ is separable Banach space and finally we construct $\mcZ^p[\mcB]$.

12 pages. Constructive comments expected from expert of this area. arXiv admin note: text overlap with arXiv:2002.11512