BMO-space for non-absolute integrable functions

Hemanta Kalita, Bipan Hazarika


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.


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