Đề tài " Cm extension by linear operators "

Introduction and statement of results Let E ⊂ Rn , and m ≥ 1. We write C m (E) for the Banach space of all real-valued functions ϕ on E such that ϕ = F on E for some F ∈ C m (Rn ). The natural norm on C m (E) is given by ϕ C m (E) = inf{ F C m (Rn ) : F ∈ C m (Rn ) and F = ϕ on E} . Here, as usual, C m (Rn ) is the space of real-valued functions on Rn with continuous and bounded derivatives through order m; and F C m (Rn ) = |β|≤m x∈Rn max sup |∂ β F (x)| .