Historical Note
According to Nirenberg (1985, p. 703 and p. 707), the space of functions of bounded mean oscillation was introduced by John (1961, pp. 410–411) in connection with his studies of mappings from a bounded set belonging to ℝn into ℝn and the corresponding problems arising from elasticity theory, precisely from the concept of elastic strain: the basic notation was introduced in a closely following paper by John & Nirenberg (1961), where several properties of this function spaces were proved. The next important step in the development of the theory was the proof by Charles Fefferman of the duality between BMO and the Hardy space H1, in the noted paper Fefferman & Stein 1972: a constructive proof of this result, introducing new methods and starting a further development of the theory, was given by Akihito Uchiyama.
Read more about this topic: Bounded Mean Oscillation
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