In mathematics, the Besov space (named after Oleg Vladimirovich Besov) is a complete quasinormed space which is a Banach space when 1 ≤ p, q ≤ ∞. It, as well as the similarly defined Triebel–Lizorkin space, serve to generalize more elementary function spaces and are effective at measuring (in a sense) smoothness properties of functions.
and define the modulus of continuity by
Let n be a non-negative integer and define: s = n + α with 0 < α ≤ 1. The Besov space contains all functions f such that
The Besov space is equipped with the norm
The Besov spaces coincide with the more classical Sobolev spaces .
If then .
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- DeVore, R., Kyriazis, G. and Wang, P. "Multiscale characterizations of Besov spaces on bounded domains", Journal of Approximation Theory 93, 273-292 (1998).
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