THE SHARP JACKSON INEQUALITY FOR L^2-APPROXIMATION ON THE PERIODIC CYLINDER

摘要

We consider Jackson inequality in L^2(B^d × T,W_(κ,μ)~B(x)),where the weight function W_(κ,μ)~B(x) is defined on the ball B^d and related to reflection group,and obtain the sharp Jackson inequality E_(n- 1,m-1)(f)2 ≤k_(n,m)(r,r)ω_r(f,t)_2,T ≥ 2τ_(n,λ),where τ_(n,λ) is the first positive zero of the Gegenbauer cosine polynomial C_n~λ(cosθ)(n ∈ N).