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 the modulus of continuity is defined 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 .
- Triebel, H. "Theory of Function Spaces II".
- Besov, O. V. "On a certain family of functional spaces. Embedding and extension theorems", Dokl. Akad. Nauk SSSR 126 (1959), 1163–1165.
- DeVore, R. and Lorentz, G. "Constructive Approximation", 1993.
- Weisstein, Eric W. "Besov Space." From MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/BesovSpace.html
- DeVore, R., Kyriazis, G. and Wang, P. "Multiscale characterizations of Besov spaces on bounded domains", Journal of Approximation Theory 93, 273-292 (1998).
|This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.|