The sharp jackson inequality for L2-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(τ,r)wr(f,t)2,τ≥2τn,λ,En−1,m−1(f)2≤Kn,m(τ,r)wr(f,t)2,τ≥2τn,λ,where τn,λτn,λ is the first positive zero of the Gegenbauer cosine polynomial Cnλ(cosθ)(n∈ℕ).