# An embedding relation for bounded mean oscillation on rectangles

## TL;DR

This paper investigates the properties of a specific function space called mean little BMO in a two-parameter setting, showing it is a strict subset of the Cotlar-Sadosky space, with implications for harmonic analysis.

## Contribution

It establishes that the Cotlar-Sadosky space of bounded mean oscillation functions is a proper subset of the mean little BMO space in the two-parameter context.

## Key findings

- Mean little BMO is introduced for functions on rectangles.
- The Cotlar-Sadosky space is shown to be a strict subspace of mean little BMO.
- Results relate to the multiplier algebra of product BMO.

## Abstract

In the two-parameter setting, we say a function belongs to the mean little $BMO$, if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by S. Pott and the author in relation with the multiplier algebra of the product $BMO$ of Chang-Fefferman. We prove that the Cotlar-Sadosky space of functions of bounded mean oscillation $bmo(\mathbb{T}^N)$ is a strict subspace of the mean little $BMO$.