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

We consider Jackson inequality in L2(Bd × T,Wκ,μB（x）),where the weight function Wκ,μB（x） is defined on the ball Bd and related to reflection group,and obtain the sharp Jackson inequality En- 1,m-1（f）2 ≤kn,m（r,r）ωr（f,t）2,T ≥ 2τn,λ,where τn,λ is the first positive zero of the Gegenbauer cosine polynomial Cnλ（cosθ）（n ∈ N）.