The Besov subspace consisting of most non-smooth functions

Under the assumptions that Δ(f, h)(t) = |f(t + h) − f(t)|, X is a symmetric space of functions in 0, 1], α ∈ (0, 1) and p ∈ 1, ∞) are any fixed number, by the triple (X, α, p) a Besov type space Λ _X,p ^α is constructed, where the norm is given by the equality For any α ₀ ∈ (0, 1), it is shown that there exists an infinite-dimensional, closed subspace of Λ _X,p ^α0, such that any non-identically zero function does not belong to the subspace Λ _X,p ^α with α > α ₀. The work is done under the financial support of RFFI, Project Cod 08-01-00669