Bounded Mean Oscillation
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In harmonic analysis, a branch of mathematics, the space of functions of bounded mean oscillation (BMO), introduced by John & Nirenberg (1961), plays the same role in the theory of Hardy spaces that the space L of bounded functions plays in the theory of Lp-spaces. A general reference for functions of bounded mean oscillation is (Stein 1993, chapter IV).The space VMO of functions of vanishing mean oscillation is the closure in BMO of the continuous functions that vanish at infinity. It can also be defined as the space of functions whose "mean oscillations" on balls Q are not only bounded, but ...
In harmonic analysis, a branch of mathematics, the space of functions of bounded mean oscillation (BMO), introduced by John & Nirenberg (1961), plays the same role in the theory of Hardy spaces that the space L of bounded functions plays in the theory of Lp-spaces. A general reference for functions of bounded mean oscillation is (Stein 1993, chapter IV).The space VMO of functions of vanishing mean oscillation is the closure in BMO of the continuous functions that vanish at infinity. It can also be defined as the space of functions whose "mean oscillations" on balls Q are not only bounded, but also tend to zero uniformly as the radius of the ball Q tends to 0 or infinity. The space VMO is a sort of Hardy space analogue of the space of continuous functions vanishing at infinity, and in particular the Hardy space H1 is the dual of VMO. (Stein 1993, p. 180)
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