Gaussian averages of interpolated bodies and applications to approximate reconstruction

Abstract

We prove sharp bounds for the expectation of the supremum of the Gaussian process indexed by the intersection of Bpn with ρ Bqn for 1 ≤ p, q ≤ ∞ and ρ > 0, and by the intersection of Bp ∞n with ρ B2n for 0 < p ≤ 1 and ρ > 0. We present an ap