John l tomkinson biography definition

In harmonic analysis in mathematics, a function of bounded mean oscillation, also known as a BMO function, is a real-valued function whose mean oscillation is bounded (finite).

The space of functions of bounded mean oscillation (BMO), is a function space that, in some precise sense, plays the same role in the theory of Hardy spacesH^p that the space L^∞ of essentially bounded functions plays in the theory of L^p-spaces: it is also called John–Nirenberg space, after Fritz John and Louis Nirenberg who introduced and studied it for the first time.

Historical note

According to Nirenberg (1985, p. 703 and p. 707),^[1] 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 into and the corresponding problems arising from elasticity theory, precisely from the concept of elastic strain: the basic notation was