On strong tractability of weighted multivariate integration

We prove that for every dimension s and every number n of points, there exists a point-set P_n,s whose γ-weighted unanchored L _∞ discrepancy is bounded from above by C(b)/n^1/2-b independently of s provided that the sequence γ = {γ_k} has ∑_k=1^∞ γ_k^a for some (even arbitrarily large) a. Here 6 is a positive number that could be chosen arbitrarily close to zero and C(b) depends on b but not on s or n. This result yields strong tractability of the corresponding integration problems including approximation of weighted integrals ∫_Df(x)ρ(x)dx over unbounded domains such as D = ℝ^s. It also supplements the results that provide an upper bound of the form C√s/n when γ_k ≡ 1.