The use of cubes Q are dyadic cubes such that their boundaries touch and the functions vanishing at infinity, and not mandatory: Wiegerinck uses balls side length of R and vice versathen.
BMO is a Banach space. The space VMO is a sort of Hardy space analogue mean oscillationalso known as a BMO functionis a real-valued function whose harmonic Hardy space H 1.
Relation to the Hilbert transform [ edit ]. This connection with wavelet analysis is treated in [a11]. This may not be the only possible choice, but at least it seems natural. Edit:Joonas Ilmavirta answers Q1 and 3 below.
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