On one extremal problem for numerical series - Radzievskaya, E. I.; Radzievskii, G. V. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
Let Γ be the set of all permutations of the natural series and let α = {α_j}_j ∈ ℕ, ν = {ν_j}_j ∈ ℕ, and η = η_j_j ∈ ℕ be nonnegative number sequences for which \| u (α η )_γ \|_1 : = _j = 1^∞ v _j α _γ (_j ) η _γ (_j ) is defined for all γ:= {γ(j)}_j ∈ ℕ ∈ Γ and η ∈ l_p. We find _η :\| η \|_p = 1 _γ Γ \| u (α η )_γ \|_1 in the case where 1 < p < ∞.