Besov space
In mathematics, the Besov space is a complete quasinormed space which is a Banach space when. These spaces, as well as the similarly defined Triebel–Lizorkin spaces, serve to generalize more elementary function spaces such as Sobolev spaces and are effective at measuring regularity properties of functions.Definition
Several equivalent definitions exist. One of them is given below.
Let
and define the modulus of continuity by
Let be a non-negative integer and define: with. The Besov space contains all functions such thatNorm
The Besov space is equipped with the norm
The Besov spaces coincide with the more classical Sobolev spaces.
If and is not an integer, then , where denotes the Sobolev–Slobodeckij space.
