Besov Space

A type of abstract Space which occurs in Spline and Rational Function approximations. The Besov space $B^\alpha_{p,q}$ is a complete quasinormed space which is a Banach Space when $1\leq p$, $q\leq\infty$ (Petrushev and Popov 1987).

References

Bergh, J. and Löfström, J. Interpolation Spaces. New York: Springer-Verlag, 1976.

Peetre, J. New Thoughts on Besov Spaces. Durham, NC: Duke University Press, 1976.

Petrushev, P. P. and Popov, V. A. ``Besov Spaces.'' §7.2 in Rational Approximation of Real Functions. New York: Cambridge University Press, pp. 201-203, 1987.

Triebel, H. Interpolation Theory, Function Spaces, Differential Operators. New York: Elsevier, 1978.