Besov space

In mathematics, the Besov space (named after Oleg Vladimirovich Besov)

is a complete quasinormed space which is a Banach space when 1 ≤ p, q ≤ ∞.

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.

Several equivalent definitions exist.

This definition is quite limited because it does not extend to the range s ≤ 0.

Let and define the modulus of continuity by Let n be a non-negative integer and define: s = n + α with 0 < α ≤ 1.

contains all functions f such that The Besov space

is equipped with the norm The Besov spaces

coincide with the more classical Sobolev spaces

denotes the Sobolev–Slobodeckij space.

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