A Besov space named after Oleg Vladimirovich Besov, is a complete quasinormal space which is a Banach space when $$1 \leq p, q \leq \infty$$. 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.