BMO-space for non-absolute integrable functions

Abstract

The functions with bounded mean oscillation (BMO) have been shown to be  immense interest in several areas of analysis and probability. We introduce BMO-type space $BMO_{HK}(\R^n)$ for non-absolute integrable functions. Various properties and completion of $BMO_{HK} (\mathbb{R}^n )$ are included. Relations between the classical $BMO$ space and $BMO_{HK} (\mathbb{R}^n )$ are investigated.