Multivariate integration in C^\infty([0,1]^d) is not strongly tractable

Abstract

It has long been known that the multivariate integration problem for the unit ball in $C^r([0,1]^d)$ is intractable for fixed finite $r$. H. Woźniakowski has recently conjectured that this is true even if $r=\infty$. This paper establishes a partial result in this direction. We prove that the multivariate integration problem, for infinitely differential functions all of whose variables are bounded by one, is not strongly tractable.