An embedding relation for bounded mean oscillation on rectangles
Volume 112 / 2014
Annales Polonici Mathematici 112 (2014), 287-299
MSC: Primary 42B15, 32A37; Secondary 42B35.
DOI: 10.4064/ap112-3-6
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 present author in relation to the multiplier algebra of the product BMO of Chang–Fefferman. We prove that the Cotlar–Sadosky space ${\rm bmo}(\mathbb {T}^N)$ of functions of bounded mean oscillation is a strict subspace of the mean little BMO.
