The Besov Subspace Consisting of Most Non-Smooth Functions

摘要

Under the assumptions that △(f, h)(t) = ∣f(t+ h)-f(t)∣, X is a symmetric space of functions in [0,1],α ∈(0,1) and p∈[l,∞) are any fixed number, by the triple (X, α,p) a Besov type space Λ_X~α,p is constructed, where the norm is given by the equalityrn‖f∣Λ_χ~α,p‖=(∑_(i=1)~∞(2~(αi)‖△(f;2~(-i)(·)∣X‖)~p)~(1/p)rnFor any α_0∈ (0,1), it is shown that there exists an infinite-dimensional, closed subspace of Λ_χ~(α_0),p such that any non-identically zero function does not belong to the subspace Λ_χ~α,p with α>α_0.