On functions of bounded β-dimensional mean oscillation

Abstract In this paper, we define a notion of β-dimensional mean oscillation functions u : Q 0 ⊂ ℝ d → {u:Q_{0}\subset\mathbb{R}^{d}\to\mathbb{R}} which are integrable on subsets the cube {Q_{0}} : ∥ BMO β ⁢ ( stretchy="false">) := movablelimits="false">sup ⁡ movablelimits="false">inf c ∈ 1 l largeop="true" symmetric="true">∫ stretchy="false">| - rspace="4.2pt"